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16 results on '"Olaf Wagner"'

1. A METRIC VERSION OF SCHLICHTING’S THEOREM

Author

Frank Olaf Wagner and Itaï Ben Yaacov

Subjects
Philosophy, Pure mathematics, 010201 computation theory & mathematics, Logic, 010102 general mathematics, 0102 computer and information sciences, 0101 mathematics, Invariant (mathematics), 01 natural sciences, Mathematics
Abstract

If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

Published
2020
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2. Largeness and equational probability in groups

Author

Frank Olaf Wagner, Khaled Jaber, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Group Theory (math.GR), Mathematical proof, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Combinatorics, Set (abstract data type), 0103 physical sciences, FOS: Mathematics, largeness, 0101 mathematics, Link (knot theory), Mathematics, Algebra and Number Theory, Group (mathematics), Applied Mathematics, 010102 general mathematics, Probabilistic logic, 20A15, 03C60, 20P99, Mathematics - Logic, 16. Peace & justice, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], probabilistic group theory, Inner measure, 010307 mathematical physics, Geometry and Topology, Logic (math.LO), Mathematics - Group Theory, Value (mathematics), Analysis, Group theory
Abstract

We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets. We link this with the inner measure of the set of solutions of an equation in a group, leading to new results and/or proofs in equational probabilistic group theory., Comment: Annales math{\'e}matiques Blaise Pascal, cedram, In press

Published
2020

3. À LA RECHERCHE DU TORE PERDU

Author

Thomas Blossier, Frank Olaf Wagner, Amador Martin-Pizarro, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), ANR-09-BLAN-0047,MODIG,Théorie des modèles et interactions avec la géométrie / Model Theory and interactions with geometry(2009), and ANR-13-BS01-0006,ValCoMo,Valuations, Combinatoire et Théorie des Modèles(2013)

Subjects
Model Theory, Logic, bad field, 010102 general mathematics, amalgamation method, 01 natural sciences, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Philosophy, 03C45, Algebraic group, 0103 physical sciences, bad group, group, algebraic group, 010307 mathematical physics, 0101 mathematics, Humanities, interpretation, flatness, Mathematics, Flatness (mathematics)
Abstract

International audience; We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic.; Un groupe interprétable dans le mauvais corps vert est isogène à un quotient d'un sous-groupe définissable d'un groupe algébrique par une puissance du groupe vert. Un sous-groupe définissable d'un groupe algébrique dans un corps vert ou rouge est une extension des points colorés d'un groupe algébrique multiplicatif ou additif par un groupe algébrique. En particulier, tout groupe simple définissable dans un corps coloré est algébrique.

Published
2016
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4. Dimensional groups and fields

Author

Frank Olaf Wagner, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and ANR-13-BS01-0006,ValCoMo,Valuations, Combinatoire et Théorie des Modèles(2013)

Subjects
Pure mathematics, Study groups, Logic, Group (mathematics), Carry (arithmetic), 010102 general mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Mathematics - Logic, 0102 computer and information sciences, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Philosophy, Mathematics::Logic, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Chain (algebraic topology), Dimension (vector space), 010201 computation theory & mathematics, Domain (ring theory), MSC 03C45, 03C20, 03C60, 12L12, 20F24, FOS: Mathematics, 0101 mathematics, Logic (math.LO), Mathematics
Abstract

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite $\widetilde {\mathfrak M}_c$ -group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.

Published
2018

5. Quelques réflexions inévitables

Author

Frank Olaf Wagner

Subjects
Pure mathematics, Logic, 010102 general mathematics, 16. Peace & justice, 01 natural sciences, Philosophy, Simple (abstract algebra), 0103 physical sciences, Calculus, 010307 mathematical physics, 0101 mathematics, Algebra over a field, Stable group, Mathematics
Abstract

We generalize Frecon's construction of the inevitable radical to groups in stable and even simple theories. Nous generalisons la construction de Frecon du radical inevitable aux groupes dans les theories stables et meme simples.

Published
2012
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6. A Fitting Theorem for Simple Theories

Author

Frank Olaf Wagner, Daniel Palacín, Institut für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms-Universität Münster (WWU), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Algèbre, géométrie, logique (AGL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), SFB 878 and project MTM 2011-26840, and ANR-13-BS01-0006,ValCoMo,Valuations, Combinatoire et Théorie des Modèles(2013)

Subjects
Pure mathematics, Index (economics), General Mathematics, 03C45, 20F18, 20F24, 20F12, 20F19, Group Theory (math.GR), 01 natural sciences, Fitting subgroup, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Mathematics::Group Theory, Simple (abstract algebra), 0103 physical sciences, nilpotent, FOS: Mathematics, group, 0101 mathematics, Mathematics, Group (mathematics), 010102 general mathematics, Mathematics - Logic, Nilpotent, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Bounded function, 010307 mathematical physics, simple theory, Logic (math.LO), Mathematics - Group Theory
Abstract

International audience; The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup.

Published
2014
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7. SUPERSIMPLICITY AND QUADRATIC EXTENSIONS

Author

Frank Olaf Wagner, Amador Martin-Pizarro, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Reymond, Aurélie, and DFG-Forschungsstipendium MA3310/1-1

Subjects
Logic, Computer Science::Neural and Evolutionary Computation, Physics::Medical Physics, Physics::Optics, Field (mathematics), 0102 computer and information sciences, 01 natural sciences, Supersimplicity, Generic point, 03C45, Quadratic equation, Modular elliptic curve, 0101 mathematics, Mathematics, Discrete mathematics, Fields, Model Theory, 010102 general mathematics, 16. Peace & justice, Twists of curves, Philosophy, Elliptic curve point multiplication, Elliptic curve, Mathematics::Logic, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], 010201 computation theory & mathematics, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], Tripling-oriented Doche–Icart–Kohel curve
Abstract

International audience; An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point.

Published
2013
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8. Small, $nm$-stable compact $G$-groups

Author

Krzysztof Krupiński, Frank Olaf Wagner, Instytut Matematyczny, Uniwersytet Wroclawski, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), European Project: 28407,MODNET, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Profinite group, Conjecture, Inverse system, General Mathematics, 010102 general mathematics, Mathematics - Logic, 0102 computer and information sciences, Group Theory (math.GR), MSC 2010 : 03C45, 20E18, 54H11, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Combinatorics, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Polish structure, 010201 computation theory & mathematics, FOS: Mathematics, Small compact $G$-group, Inverse limit, 0101 mathematics, Algebra over a field, Arithmetic, Logic (math.LO), Mathematics - Group Theory, Mathematics
Abstract

International audience; We prove that if $(H,G)$ is a small, $nm$-stable compact $G$-group, then $H$ is nilpotent-by-finite, and if additionally $\NM(H) \leq \omega$, then $H$ is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, $nm$-stable compact $G$-group is abelian-by-finite. We give examples of small, $nm$-stable compact $G$-groups of infinite ordinal $\NM$-rank, providing counter-examples to the $\NM$-gap conjecture.

Published
2013
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9. Elimination of Hyperimaginaries and Stable Independence in Simple CM-Trivial Theories

Author

Frank Olaf Wagner, Daniel Palacín, Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona (UB), Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MTM 2008-0154 (Spain), 2009SGR 00187 (Catalunia), and ANR-09-BLAN-0047,MODIG,Théorie des modèles et interactions avec la géométrie / Model Theory and interactions with geometry(2009)

Subjects
Logic, independence, 0102 computer and information sciences, 01 natural sciences, elimination, 03C45, Simple (abstract algebra), MSC 03C45, FOS: Mathematics, CM-trivial, Finitary, 0101 mathematics, hyperimaginary, Mathematics, Discrete mathematics, Sequence, 010102 general mathematics, Mathematics - Logic, stable forking, Independence relation, finitary, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], 010201 computation theory & mathematics, simple, Independence (mathematical logic), hyperimaginaries, simple theory, Logic (math.LO)
Abstract

International audience; In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.

Published
2013

10. The right angle to look at orthogonal sets

Author

Frank Olaf Wagner, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), ANR-09-BLAN-0047,MODIG,Théorie des modèles et interactions avec la géométrie / Model Theory and interactions with geometry(2009), and ANR-13-BS01-0006,ValCoMo,Valuations, Combinatoire et Théorie des Modèles(2013)

Subjects
Discrete mathematics, Logic, 010102 general mathematics, Right angle, Mathematics - Logic, 0102 computer and information sciences, simplicity, 01 natural sciences, Commensurability (mathematics), Combinatorics, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Philosophy, Mathematics::Group Theory, 03C45, Commensurable groups, orthogonality, 010201 computation theory & mathematics, FOS: Mathematics, internality, Simplicity theory, 0101 mathematics, Logic (math.LO), Mathematics
Abstract

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in X ∪ Y has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developed. Moreover, a version of Schlichting’s Theorem for hyperdefinable families of commensurable subgroups is shown.

Published
2013
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11. On Variants of CM-triviality

Author

Thomas Blossier, Frank Olaf Wagner, Amador Martin-Pizarro, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and Alexander von Humboldt-Stiftung Forschungsstipendium für erfahrene Wissenschaftler 3.3-FRA/1137360 STP

Subjects
Discrete mathematics, Pure mathematics, Algebra and Number Theory, CM-triviality, analysability, 010102 general mathematics, Mathematics - Logic, 16. Peace & justice, 01 natural sciences, Triviality, Canonical Base Property, 010104 statistics & probability, Nilpotent, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Mathematics::Logic, MSC 03C45, FOS: Mathematics, internality, 0101 mathematics, Invariant (mathematics), Logic (math.LO), Quotient, Mathematics
Abstract

International audience; We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.

Published
2012
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12. Around Podewski's conjecture

Author

Krzysztof Krupiński, Predrag Tanović, Frank Olaf Wagner, Instytut Matematyczny, Uniwersytet Wroclawski, Mathematical Institute, Serbian Academy of Sciences and Arts (SASA), Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and Supported by the Polish Government grant N N201 545938, and the Ministry of Education and Science of Serbia.

Subjects
Field (mathematics), 0102 computer and information sciences, minimal group, 01 natural sciences, Prime (order theory), Combinatorics, FOS: Mathematics, Order (group theory), 0101 mathematics, Abelian group, Algebraically closed field, minimal field, valued group, Mathematics, Algebra and Number Theory, Conjecture, Group (mathematics), 010102 general mathematics, Mathematics - Logic, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], 010201 computation theory & mathematics, MSC 03C60, 12L12, 20A15, 03C45, Exponent, Podewski's Conjecture, Logic (math.LO), Primary 03C60, Secondary 12L12, 20A15, 03C45
Abstract

A long-standing conjecture of Podewski states that every minimal field is algebraically closed. It was proved by Wagner for fields of positive characteristic, but it remains wide open in the zero-characteristic case. We reduce Podewski's conjecture to the case of fields having a definable (in the pure field structure), well partial order with an infinite chain, and we conjecture that such fields do not exist. Then we support this conjecture by showing that there is no minimal field interpreting a linear order in a specific way; in our terminology, there is no almost linear, minimal field. On the other hand, we give an example of an almost linear, minimal group $(M, Comment: 16 pages

Published
2012
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13. Artin-Schreier extensions in NIP and simple fields

Author

Itay Kaplan, Thomas Scanlon, and Frank Olaf Wagner

Subjects
Discrete mathematics, Computer Science::Machine Learning, Mathematics::Functional Analysis, General Mathematics, 010102 general mathematics, Field (mathematics), 06 humanities and the arts, Extension (predicate logic), Mathematics - Logic, 0603 philosophy, ethics and religion, 01 natural sciences, Statistics::Machine Learning, Mathematics::Logic, Mathematics::Group Theory, Simple (abstract algebra), 060302 philosophy, FOS: Mathematics, NIP, 0101 mathematics, Algebra over a field, Logic (math.LO), Finite set, Mathematics
Abstract

We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.

Published
2010

14. Die böse Farbe

Author

Frank Olaf Wagner, Andreas Baudisch, Martin Hils, Amador Martin-Pizarro, Institut für Mathematik [Berlin], Technical University of Berlin / Technische Universität Berlin (TU), Equipe de Logique Mathématique (ELM), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Algèbre, géométrie, logique (AGL), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), European Project, Technische Universität Berlin (TU), Equipe de Logique Mathématique, Institut de Mathématiques de Jussieu (IMJ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Model theory, Pure mathematics, 03C45, 12L12, 20F11, General Mathematics, 010102 general mathematics, Multiplicative function, collaps, Zero (complex analysis), green field, Field (mathematics), 0102 computer and information sciences, amalgamation construction, 01 natural sciences, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Dimension (vector space), 010201 computation theory & mathematics, bad fields, 0101 mathematics, Algebraically closed field, Construct (philosophy), Mathematics
Abstract

ZusammenfassungWir konstruieren einen schlechten Körper der Charakteristik Null. Mit anderen Worten, wir konstruieren einen algebraisch abgeschlossenen Körper mit einem Dimensionsbegriff analog der Zariski-Dimension, zusammen mit einer unendlichen echten multiplikativen Untergruppe der Dimension Eins, so daβ der Körper selbst Dimension Zwei hat. Dies beantwortet eine alte Frage von Zilber.

Published
2009
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15. Some remarks on one-basedness

Author

Frank Olaf Wagner, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
stable, Logic, 010102 general mathematics, Mathematics::History and Overview, 0102 computer and information sciences, Mathematics - Logic, 01 natural sciences, Computer Science::Computers and Society, one-based, Philosophy, Physics::Popular Physics, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], 03C45, analysable, 010201 computation theory & mathematics, simple, internal, FOS: Mathematics, Mathematics education, 0101 mathematics, Logic (math.LO), Mathematics
Abstract

A type analysable in one-based types in a simple theory is itself one-based.

Published
2004
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16. Liftez les Sylows! Une suite \'a 'Sous-groupes periodiques d'un groupe stable'

Author

Frank Olaf Wagner and Bruno Poizat

Subjects
Combinatorics, Philosophy, Logic, Group (mathematics), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, 010102 general mathematics, 0103 physical sciences, 010307 mathematical physics, 0101 mathematics, 01 natural sciences, Mathematics - Group Theory, Mathematics
Abstract

If G is an omega-stable group with a normal definable subgroup H, then the Sylow-2-subgroups G/H are the images of the Sylow-2-subgroups of G.Zusammenfassung. Sei G eine omega-stabile Gruppe und H ein definierbarer Normalteiler von G. Dann sind die Sylow-2-Untergruppen von G/H Bilder der Sylow-2-Untergruppen von G.

Published
1998

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