Search

We present a manuscript of Paul Lorenzen that provides a proof of consistency for elementary number theory as an application of the construction of the free countably complete pseudocomplemented se...

International audience; Paul Lorenzen, mathematician and philosopher of the 20th century, mentions October 1947 as the date of a crisis in his mathematical and philosophical investigations. An autograph dated 15 October 1947 documents this crisis. This article proposes a translation and a commentary of it and sketches the circumstances of its writing on the base of his correspondence with Paul Bernays. A letter from Lorenzen to Carl Friedrich Gethmann dated 14 January 1988 carves out the story of this crisis by showing how he soaks up the indications of his correspondents and transmutes them into an absolutely original research. [Paul Lorenzen, mathématicien et philosophe du 20e siècle, évoque le mois d'octobre 1947 comme la date d'une césure dans ses investigations tant mathématiques que philosophiques. Un écrit autographe daté du 15 octobre 1947 marque cette césure. Cet article en propose une traduction et un commentaire ligne à ligne, puis esquisse les circonstances de son écriture sur la base de la correspondance avec Paul Bernays, figure tutélaire de la logique mathématique et l'un de ses principaux interlocuteurs à cette époque, à l'instar de Heinrich Scholz et Oskar Becker. Une lettre de Lorenzen à Carl Friedrich Gethmann datée du 14 janvier 1988 étoffe le récit de cette césure en montrant comment il s'imprègne des indications que lui fournissent ses correspondants pour les transmuter en une recherche absolument originale.]; Paul Lorenzen, mathématicien et philosophe du 20e siècle, évoque le mois d'octobre 1947 comme la date d'une césure dans ses investigations tant mathématiques que philosophiques. Un écrit autographe daté du 15 octobre 1947 marque cette césure. Cet article en propose une traduction et un commentaire ligne à ligne, puis esquisse les circonstances de son écriture sur la base de la correspondance avec Paul Bernays, figure tutélaire de la logique mathématique et l'un de ses principaux interlocuteurs à cette époque, à l'instar de Heinrich Scholz et Oskar Becker. Une lettre de Lorenzen à Carl Friedrich Gethmann datée du 14 janvier 1988 étoffe le récit de cette césure en montrant comment il s'imprègne des indications que lui fournissent ses correspondants pour les transmuter en une recherche absolument originale.

International audience; This essay inquires how mathematical beings could be inserted into the architecture of modes of existence proposed by Bruno Latour in the framework of his pluralist and renewed ontology of the modern world. An answer to this question is put forward with the aid of the work of Reviel Netz on the emergence of Greek mathematics, and of Charles Sanders Peirce on the diagrammatic dimension of mathematical practice, in the framework of an empiric conception of mathematics based on the notion of experience according to William James, and inspired by certain aspects of Per Martin-Löf's philosophy. It provides a way of describing the firm certainty with which proofs endow theorems, while invalidating the interpretation of this certainty as the mark of a direct access to an absolute and transcendental truth.; L'objet de cet essai est l'accueil des entités mathématiques dans l'architecture des modes d'existence proposée par Bruno Latour dans le cadre de son ontologie pluraliste du monde moderne. Les travaux de Reviel Netz sur l'émergence des mathématiques grecques et de Charles Sanders Peirce sur la dimension diagrammatique de l'activité mathématique sont employés pour proposer une réponse dans le cadre d'une conception empirique des mathématiques basée sur la notion d'expérience chère à William James et inspirée par certains aspects de la philosophie de Per Martin-Löf. Cette approche permet de penser la solide certitude dont la démonstration dote les résultats mathématiques tout en invalidant son interprétation comme la marque d'un accès direct à une vérité absolue et transcendante.

International audience; We provide constructive versions of Hilbert's syzygy theorem for Z and Z/nZ following Schreyer's method. Moreover, we extend these results to arbitrary coherent strict Bézout rings with a divisibility test for the case of finitely generated modules whose module of leading terms is finitely generated.

Let R be a local domain, v a valuation of its quotient field centred in R at its maximal ideal. We investigate the relationship between R h , the henselisation of R as local ring, and v ˜ , the henselisation of the valuation v, by focussing on the recent result by de Felipe and Teissier referred to in the title. We give a new proof that simplifies the original one by using purely algebraic arguments. This proof is moreover constructive in the sense of Bishop and previous work of the authors, and allows us to obtain as a by-product a (slight) generalisation of the theorem by de Felipe and Teissier.

Krull’s Fundamentalsatz, the generalisation of the main theorem of elementary number theory to integral domains, is the starting point of Lorenzen’s career in mathematics. This article traces a conceptual history of Lorenzen’s successive reformulations of the Fundamentalsatz on the basis of excerpts of his articles. An edition of the extant correspondence of Lorenzen with Hasse, Krull, and Aubert provides a better understanding of the context of these investigations.

Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure. We also describe equivariant systems of ideals à la Lorenzen and show that the remarkable regularisation process he invented yields a regular entailment relation. By providing constructive objects and arguments, we pursue Lorenzen’s aim of “bringing to light the basic, pure concepts in their simple and transparent clarity”.

We propose an edition of the reports on Paul Lorenzen’s Ph.D. thesis by Helmut Hasse and Carl Ludwig Siegel, of the known correspondence of Lorenzen with Hasse, Wolfgang Krull, and Karl Egil Aubert, and of a relevant letter from Krull to Heinrich Scholz. It provides evidence for the circumstances in which Lorenzen comes to his insights during the studied period of time.

International audience; Unbounded entailment relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental rôle in logic (see Scott 1974) and in algebra (see Lombardi and Quitté 2015). We call “systems of ideals” their single-conclusion counterpart. If they preserve the order of a commutative ordered monoid G and are equivariant w.r.t. its law, we call them “equivariant systems of ideals for G”: they describe all morphisms from G to meet-semilattice-ordered monoids generated by (the image of) G. Taking an article by Lorenzen (1953) as a starting point, we also describe all morphisms from a commutative ordered group G to lattice-ordered groups generated by G through unbounded entailment relations that preserve its order, are equivariant, and satisfy a regularity property invented by Lorenzen (1950); we call them “regular entailment relations”. In particular, the free lattice-ordered group generated by G is described through the finest regular entailment relation for G, and we provide an explicit description for it; it is order-reflecting if and only if the morphism is injective, so that the Lorenzen-Clifford-Dieudonné theorem fits into our framework. Lorenzen’s research in algebra starts as an inquiry into the system of Dedekind ideals for the divisibility group of an integral domain R, and specifically into Wolfgang Krull’s “Fundamentalsatz” that R may be represented as an intersection of valuation rings if and only if R is integrally closed: his constructive substitute for this representation is the “regularisation” of the system of Dedekind ideals, i.e. the lattice-ordered group generated by it when doing as if its elements are comparable.

This text presents the economic forecast released by the KOF Swiss Economic Institute at ETH Zurich on 26 March 2015. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. Then we turn to the international economy and its effects on Switzerland and look into the Swiss economy in more detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and figures, such as employment and unemployment, the price level and the exchange rate. For the 2015-2016 period covered by this forecast, we expect a recession stretching over the first three quarters of 2015. After this, the Swiss economy is expected to recover relatively swiftly.

This text presents the economic forecast released by the KOF Swiss Economic Institute at ETH Zurich on 12 June 2015. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. Then we turn to the international economy and its effects on Switzerland and the Swiss economy in detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and other key variables, such as employment and unemployment, the price level and the exchange rate. For the 2015/2016 period covered by this forecast, we expect a recession stretching over the first two quarters of 2015. After this, the Swiss economy should recover, but a swift return to the pre-SNB-shock growth rates is not expected.

When forecasting, all available information should be used. As the most recent indicators are mostly published in monthly or higher frequency while the GDP is released in quarterly frequency, this can pose a problem in an econometric framework. This paper presents the KOF short-term indicator for international forecasts, which uses both bridge equations as well as a MIDAS approach. The forecast performance of the models is then assessed by conducting a real-time experiment using a reduced dataset for the US. Even with this reduced set forecast performance can be increased by up to 25 percent in comparison to an autoregressive model.

This article is an invitation to read a famous text of Roger Ap{\'e}ry, "Math{\'e}matique constructive", published in the book "Penser les math{\'e}matiques: s{\'e}minaire de philosophie et math{\'e}matiques de l'{\'E}cole normale sup{\'e}rieure (J. Dieudonn{\'e}, M. Loi, R. Thom)" [arXiv:1705.05581]. It also proposes a commented bibliography for constructive mathematics and a technical note on measure theory., Comment: in French

This text presents the economic forecast released by the KOF Swiss Economic Institute at ETH Zurich on 13 June 2014. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. Then we turn to the international economy and its effects on Switzerland and the Swiss economy in detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and indicators, such as employment and unemployment, the price level and the exchange rate. For the 2014/2015 period covered by this forecast, we expect GDP growth to remain stable, along with a continuously moderately positive evolution of average per capita income.

This text contains the autumn forecast 2014 of the KOF Swiss Economic Institute at ETH Zurich, released on 29 October 2014. The first part discusses recent economic developments in Switzerland and abroad, and presents the main forecast results across the various sectors of the economy. Subsequently, monetary policy and fiscal policy are analyzed. In the second part, detailed forecasts for Switzerland follow, split up into the main demand components of GDP. We expect the Swiss economy to grow by 1.7% in 2015 and 2.1% in 2016, representing a small downward revision. In particular the negative development in Europe is specified as a reason for this adjustment.

This text presents the economic forecast presented by the KOF Swiss Economic Institute at ETH Zurich on 28 March 2014. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. Then we turn to the international economy and its effects on Switzerland and the Swiss economy in detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and figures, such as employment and unemployment, the price level and exchange rates. In the 2013–2015 period covered by this forecast, we expect robust GDP growth along with a moderately positive evolution of average per capita income.

This text presents the economic forecast presented by the KOF Swiss Economic Institute at the ETH Zurich on 17 December 2013. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. We then turn to the international economy and its effects on Switzerland and the Swiss economy in detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and numbers, such as employment and unemployment, the price level and the exchange rate. In the 2013 – 2015 period covered by this forecast, we expect robust GDP growth along with a positive evolution of average per capita income. The next cyclical peak will not be reached within the forecast period.

This text presents the economic forecast of the KOF Swiss Economic Institute at ETH Zurich on 23 September 2013. After an introduction describing the starting points and crucial assumptions underlying the forecast, we summarise the key results for Switzerland. Then we turn to the international economy and its effects on Switzerland and the Swiss economy in detail. For the latter, we forecast the main demand components of GDP as well as important macroeconomic prices and numbers, such as employment and unemployment, the price level and the exchange rate. In the 2013–2015 period covered by this forecast, we expect robust GDP growth along with a positive evolution of average per capita income and a cyclical peak during the winter of 2014/2015.

International audience; Cet atelier propose de rendre compte d'un cours de la troisième année de la licence de mathématiques de l'université de Franche-Comté, Musique et mathématiques, que j'organise en 2015-2016 et 2016-2017 en collaboration avec un musicien, Olivier Toulemonde, deux mathématiciens, Aurélien Galateau et Martin Meyer, une chargée de projets culturels, Lucie Vidal, et une secrétaire, Mahdya Debayle.Notre projet se concentre sur la musique improvisée, expérimentale et contemporaine. Ce choix rend compte de nos gouts musicaux, mais découle aussi du souci d'aller au-delà du contenu mathématique de l'acoustique, de l'harmonie et du rythme.Le cours est construit sur des rencontres avec des musicien.ne.s et compositeur.e.s, suivies d'un concert financé dans le cadre d'un projet du service Sciences, arts, culture de l'université. Le programme est disponible sur http://epiphymaths.univ-fcomte.fr/musique&maths et une trace numérique du cours se trouve sur http://moodle.univ-fcomte.fr/course/view.php?id=7321.Dans cet atelier, je voudrais rendre compte de cette expérience pédagogique où la table ronde fait concurrence au cours magistral, où la perception de la musique s'approfondit par un état d'esprit scientifique, et où l'activité mathématique retrouve sa nature de création artistique. Ce cours permet d'articuler des problématiques très profondes grâce à la juxtaposition de deux domaines de recherche éloignés. Je proposerai d'écouter quelques extraits musicaux pour faire émerger les questionnements de notre cours: les langages mathématiques et les langages musicaux, la liberté de la création, la précision et l'exactitude, le déterminisme, l'espace et le temps, l'émotion mathématique, la matérialité du son.Les considérations historiques se révèlent très utiles dans cette entreprise: le développement des symboliques mathématiques est mis en parallèle avec le développement des formes musicales; le développement de l'algèbre et l'arithmétisation des grandeurs illustrent les concepts de créativité et de liberté; l'histoire des mathématiques nous a aussi aidés à réfléchir à deux thèmes particuliers: l'erreur et le détournement des outils.Je montrerai aussi comment la littérature permet de jeter un pont entre musique et mathématiques.

This paper presents a MIDAS type mixed frequency VAR forecasting model. First, we propose a general and compact mixed frequency VAR framework using a stacked vector approach. Second, we integrate the mixed frequency VAR with a MIDAS type Almon lag polynomial scheme which is designed to reduce the parameter space while keeping models flexible. We show how to recast the resulting non-linear MIDAS type mixed frequency VAR into a linear equation system that can be easily estimated. A pseudo out-of-sample forecasting exercise with US real-time data yields that mixed frequency VAR substantially improves predictive accuracy upon a standard VAR for different VAR specifications. Forecast errors for, e.g., GDP growth decrease by 30 to 60 percent for forecast horizons up to six months and by around 20 percent for a forecast horizon of one year.

This paper presents a MIDAS type mixed frequency VAR forecasting model. First, we propose a general and compact mixed frequency VAR framework using a stacked vector approach. Second, we integrate the mixed frequency VAR with a MIDAS type Almon lag polynomial scheme which is designed to reduce the parameter space while keeping models fexible. We show how to recast the resulting non-linear MIDAS type mixed frequency VAR into a linear equation system that can be easily estimated. A pseudo out-of-sample forecasting exercise with US real-time data yields that the mixed frequency VAR substantially improves predictive accuracy upon a standard VAR for dierent VAR specications. Forecast errors for, e.g., GDP growth decrease by 30 to 60 percent for forecast horizons up to six months and by around 20 percent for a forecast horizon of one year.

Nous etudions le rapport entre la croissance d'une suite d'entiers et les proprietes harmoniques et fonctionnelles de la suite de caracteres associee. Nous montrons en particulier que toute suite polynomiale, ainsi que la suite des nombres premiers, contient un ensemble Λ(p) pour tout p qui n'est pas de Rosenthal.

We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property UMAP in terms of ``block unconditionality''. Then we focus on translation invariant subspaces $L^p_E(T)$ and $C_E(T)$ of functions on the circle and express block unconditionality as arithmetical conditions on $E$. Our work shows that the spaces $L^p_E(T)$, $p$ an even integer, have a singular behaviour from the almost isometric point of view: property UMAP does not interpolate between spaces $L^p_E(T)$ and $L^{p+2}_E(T)$. These arithmetical conditions are used to construct counterexamples for several natural questions and to investigate the maximal density of such sets $E$. We also prove that if $E=\{n_k\}_{k\ge1}$ with $|n_{k+1}/n_k|\to\infty$, then $C_E(T)$ has UMAP and we get a sharp estimate of the Sidon constant of Hadamard sets. Finally, we investigate the relationship of metric unconditionality and probability theory., Error in proof of Th. 8.3 (now 10.3.1) fixed. Ajout d'une introduction en francais

Releases of the GDP are subject to revisions over time. This paper examines the predictability of German GDP revisions using forecast rationality tests. Previous studies of German GDP covering data until 1997 finds that revisions of real seasonally adjusted GDP are predictable. This paper uses a newly available real-time data to analyze the revisions of real seasonal adjusted GDP, of nominal unadjusted GDP, of the seasonal pattern, and of the GDP deflator for the period between 1992 and 2006. We find that the revisions of the nominal unadjusted GDP are unpredictable, but that the revisions of the price adjustments are predictable. Nevertheless, revisions of real seasonally adjusted GDP are hardly predictable and less well predictable compared to earlier studies. This lower predictability seems to be linked to the finding that revisions of seasonal adjustments are hardly predictable, too, and that their predictability decreased over time

Globalization has intensified competition throughout industries. Product lifecycles have shortened dramatically. As pharmaceutical firms are characterized by particularly high R&D upfront costs, long before any revenues can be expected, the consequences of shorter periods to reap the rewards is particularly high.

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets; unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum, that is, by a subset of the group; the norm of the Hilbert transform and the Riesz projection on Schatten-von-Neumann classes with exponent a power of 2; the norm of Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less than 1., Comment: Corresponds to the version published in the Canadian Journal of Mathematics 63(5):1161-1187 (2011)

Background: Reliable PCR amplification of DNA fragments is the prerequisite for most genetic assays. We investigated the impact of G-quadruplex– or i-motif–like sequences on the reliability of PCR-based genetic analyses. Methods: We found the sequence context of a common intronic polymorphism in the MEN1 gene (multiple endocrine neoplasia I) to be the cause of systematic genotyping errors by inducing preferential amplification of one allelic variant [allele dropout (ADO)]. Bioinformatic analyses and pyrosequencing-based allele quantification enabled the identification of the underlying DNA structures. Results: We showed that G-quadruplex– or i-motif–like sequences can reproducibly cause ADO. In these cases, amplification efficiency strongly depends on the PCR enzyme and buffer conditions, the magnesium concentration in particular. In a randomly chosen subset of candidate single-nucleotide polymorphisms (SNPs) defined by properties deduced from 2 originally identified ADO cases, we confirmed preferential PCR amplification in up to 50% of the SNPs. We subsequently identified G-quadruplex and i-motifs harboring a SNP that alters the typical motif as the cause of this phenomenon, and a genomewide search based on the respective motifs predicted 0.5% of all SNPs listed by dbSNP and Online Mendelian Inheritance in Man to be potentially affected. Conclusions: Undetected, the described phenomenon produces systematic errors in genetic analyses that may lead to misdiagnoses in clinical settings. PCR products should be checked for G-quadruplex and i-motifs to avoid the formation of ADO-causing secondary structures. Truly affected assays can then be identified by a simple experimental procedure, which simultaneously provides the solution to the problem. .

International audience; Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda.

For an m×n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3⩽mns(AAtA), where At is the transpose of A, and s(·) is the sum of the entries. We extend this result to finite products of the form AAtAAt⋯A or AAtAAt⋯At and give some applications to the theory of iterated kernels.

Bayer ist ein diversifiziertes, internationales Unternehmen der chemisch-pharmazeutischen Industrie. Kommunikation zu allen — internen wie externen -Stakeholdergruppen nimmt fur den Konzern und seine Einheiten traditionell einen hohen Stellenwert ein.

We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer, we find a sufficient condition in terms of trails on a bipartite graph. We also establish an optimal density condition and present a random construction of bipartite graphs. As a byproduct, we get a new proof for a theorem of Erdos on circuits in graphs., 14 pages

We characterize the 1-unconditional subsequences of the canonical basis (e_rc) of elementary matrices in the Schatten-von-Neumann class S^p . The set I of couples (r,c) must be the set of edges of a bipartite graph without cycles of even length 4, 29 pages. This new version computes explicitly certain unconditionality constants, shows how our results generalize Varopoulos' work on V-Sidon sets, investigates the metric unconditional approximation property in the same context

Im Mittelpunkt der vorliegenden Untersuchung steht die Identifizierung und Bewertung der organisatorischen Gestaltungsalternativen, die in Abhangigkeit von der Beschaftigtenkategorie rechts vertraglich zur Verfugung stehen. In den vorstehenden Kapiteln wurde gezeigt, welche Organisationsoptionen bei der Wahl verschiedener Handlungstragerkategorien zulassig sind und gegebenenfalls besonders durch das Recht unterstutzt werden. Im Anschlus daran wurden diese Organisationsauspragungen einer Effizienzanalyse unterzogen.

Im vorstehenden Teil der Untersuchung wurde aufgezeigt, welche Gestaltungsalternativen der Unternehmungsorganisation bei der Beschaftigung selbstandiger bzw. abhangiger Handlungstrager rechtlich zulassig sind. Dabei haben sich fur die einzelnen organisatorischen Dimensionen — Delegation, Bereichsbildung sowie Konfiguration — deutliche Unterschiede zwischen den betrachteten Handlungstragerkategorien offenbart. Im folgenden gilt es nun, eine Bewertung des Einsatzes von selbstandig Beschaftigten bzw. von Arbeitnehmern (oder genauer: eine Bewertung der jeweils zulassigen organisatorischen Gestaltungsoptionen) vorzunehmen1.

In diesem Kapitel sind die organisatorischen Gestaltungsalternativen zu ermitteln, die unter Beachtung der Rechtsnormen zur Verfugung stehen. Gegenstand der Analyse ist dabei die Kompetenzverteilung in einem bestehenden Vertrags Verhaltnis, da (nur) hier Verteilungsspielraume auszumachen sind. Der Abschlus einer Vertragsbeziehung hingegen (als ein der Ausfuhrung vorgeschalteter Akt) setzt bekanntlich ein Vertragsangebot sowie eine gleichlautende Angebotsannahme voraus1. Der Vertragsschlus obliegt damit stets Beschaftigungsgeber und Beauftragtem gemeinsam zu gleichen Teilen. Dies gilt fur das selbstandige wie fur das abhangige Beschaftigungsverhaltnis gleichermasen, so das sich hier keine Unterschiede zwischen den Beschaftigungsformen verzeichnen lassen.

Den Schwerpunkt der vorliegenden Untersuchung bildet die Fragestellung, welche organisatorischen Gestaltungsoptionen bei der Beschaftigung selbstandiger und abhangiger Handlungstrager zur Verfugung stehen und welche Auswirkungen sich daraus fur die organisatorische Effizienz der Unternehmungsaktivitaten ergeben. Diese Thematik ist in hohem Mase anwendungsorientiert. Insofern sind auch die bisherigen Ausfuhrungen — wenngleich auf theoretisch-fundierter Basis — durch einen starken Praxisbezug gekennzeichnet. Zum Abschlus der Untersuchung soll nun in diesem Kapitel aufgezeigt werden, das mit Hilfe der erarbeiteten Ergebnisse nicht ‚nur‘ Leitlinien fur die praktische Unternehmungsgestaltung entwickelt werden konnen, sondern das sich ebenso organisationstheoretische Fragestellungen von eher grundsatzlichem Charakter beantworten lassen.

Selbstandigkeit steht fur Ungebundenheit und Handlungsfreiheit1 und bildet damit das terminologische Pendant zur Abhangigkeit. Die Bedeutung des Begriffs der Selbstandigkeit ist vielschichtig2. Es gibt nicht ‚die‘ (umfassende) Selbstandigkeit. Die Existenz in einem derartigen Zustand muste alle denkbaren Ebenen — beispielsweise geistige, kulturelle, politische, wirtschaftliche Selbstandigkeit usw. — umfassen. Sie erweist sich ebenso wie die vollstandige Abhangigkeit als theoretischer Grenzfall, der in der Realitat ausscheidet. Die Frage nach der Selbstandigkeit mus daher konkretisiert werden um die Auskunft, welche Art von Selbstandigkeit gemeint ist, d. h. an welchem spezifischen Aspekt eines Betrachtungsgegenstandes die Erhebung dieses Kriteriums anknupfen soll.

Die vorliegende Untersuchung hat sich mit der organisatorischen Komponente der Ubertragung unternehmerischer Aufgaben auf rechtlich selbstandige Handlungstrager beschaftigt. An dieser Stelle sollen nun die wesentlichen Analyseergebnisse in konzentrierter Form hervorgehoben und einer abschliesenden Wurdigung hinsichtlich ihrer praktischen Implikationen unterzogen werden. Die Arbeit schliest mit einem Ausblick.

Die vorliegende Untersuchung behandelt die Gestaltungsmoglichkeiten der Organisation der Unternehmung, die in Abhangigkeit von der gewahlten Beschaftigungsrechtsform zulassig sind. Der vielfaltig verwendete Begriff der Organisation soll hier in einem instrumentalen Sinne aufgefast werden1. Organisation umfast hiernach ein System von Regelungen, die das Verhalten der Beschaftigten auf ein ubergeordnetes Gesamtziel, das Unternehmungsziel, ausrichten sollen2. Damit bildet Organisation eines unter mehreren Merkmalen von wirtschaftlichen Handlungssystemen3. Die Unternehmung ist — neben beispielsweise ihrer Rechtsform, ihrer Grose oder ihrem Zielsystem — eben auch durch ihr spezifisches Organisationsprofil gekennzeichnet4.