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An S-Topological BE-Algebras(STBE-Algebras) is a BE-Algebra equipped with a special type of topology that makes the operation (defined on it)as S-topological continuous. In this paper, we discuss the separation axioms on a STBE-Algebras. [ABSTRACT FROM AUTHOR]

It is well-known that the square principle □λ entails the existence of a non-reflecting stationary subset of λ+, whereas the weak square principle □λ∗ does not. Here we show that if μcf(λ) < λ for all μ < λ, then □λ∗ entails the existence of a non-reflecting stationary subset of Ecf(λ)λ+ in the forcing extension for adding a single Cohen subset of λ+.It follows that indestructible forms of simultaneous stationary reflection entail the failure of weak square. We demonstrate this by settling a question concerning the subcomplete forcing axiom (SCFA), proving that SCFA entails the failure of □λ∗ for every singular cardinal λ of countable cofinality. [ABSTRACT FROM AUTHOR]

The covering property axiom CPA is consistent with ZFC: it is satisfied in the iterated perfect set model. We show that CPA implies that for every ν∈ω∪{∞} there exists a family Fν⊂Cν(R) of cardinality ω1

Satisfiability of three naturally proposed axioms, which are desirable for fuzzy inference system, was discussed by Moser and Navara in [36] . The fuzzy rule base models considered in this study were mainly the Mamdani–Assilian ones and partly also logically motivated implicative fuzzy systems. The investigation leads to the fact that often none of these fuzzy systems do satisfy the given axioms simultaneously. Therefore, Moser and Navara proposed so-called conditionally firing rules and proved that the simultaneous satisfaction of the three axioms is feasible under very mild and practically non-restrictive conditions. Note that the inference mechanism, tailored to the fuzzy rules in the investigation, was the compositional rule of inference (abb. CRI) and similarly, the concept of conditionally firing rules were stemming from the CRI and the Mamdani–Assilian model of a fuzzy rule base. For the implicative interpretation of fuzzy rules, the original axioms proposed by Moser and Navara were later on re-defined by Štěpnička and Mandal with the aim to express the meaning of the original axioms initially proposed for the Mamdani–Assilian rules. Furthermore, conditionally firing implicative rules were proposed based on the so-called Bandler–Kohout subproduct (abb. BKS) inference mechanism and a study similar to the one by Moser and Navara was undertaken for them. The study encompasses the satisfaction of the modified axioms for the use of implicative rules and the BKS. Furthermore, some additional results confirming the applicability of the conditionally firing rules satisfying the Moser–Navara axioms are also provided, including the universal approximation ability. However, the solvability criterions for fuzzy relational equations give a strong preference to the usage of the other combinations, namely, to the combination of CRI with the implicative interpretation of fuzzy rules and to the combination of BKS with the Mamdani–Assilian interpretation of fuzzy rules. Therefore, also these combinations of fuzzy inference mechanisms and interpretations of fuzzy rules should be investigated with respect to the satisfaction of Moser–Navara axioms. The main purpose of this article, which extends the short conference contribution [47] by Štěpnička, is to provide such an investigation jointly with the review on conditionally firing rules and supplementary results. [ABSTRACT FROM AUTHOR]

The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms for a class of forcings and a given ordinal ), and show that implies generic absoluteness for the first-order theory of with respect to forcings in preserving the axiom, where is a cardinal which depends on ( if is any among the classes of countably closed, proper, semiproper, stationary set preserving forcings). We also prove that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover, we outline that simultaneous generic absoluteness for with respect to and for with respect to with is in principle possible, and we present several natural models of the Morse-Kelley set theory where this phenomenon occurs (even for all simultaneously). Finally, we compare the iterated resurrection axioms (and the generic absoluteness results we can draw from them) with a variety of other forcing axioms, and also with the generic absoluteness results by Woodin and the second author. [ABSTRACT FROM AUTHOR]

We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions. For instance, we show that if κ is an uncountable cardinal such that μω < κ for every μ < κ and every AEC with L¨owenheim-Skolem number less than κ is < κ-tame, then κ is almost strongly compact. This is done by isolating a class of AECs that exhibits tameness exactly when sufficiently complete ultrafilters exist. [ABSTRACT FROM AUTHOR]

In this paper, the use of the MaxInf Principle in real optimization problems is investigated for engineering applications, where the current design solution is actually an engineering approximation. In industrial manufacturing, multibody system simulations can be used to develop new machines and mechanisms by using virtual prototyping, where an axiomatic design can be employed to analyze the independence of elements and the complexity of connections forming a general mechanical system. In the classic theories of Fisher and Wiener-Shannon, the idea of information is a measure of only probabilistic and repetitive events. However, this idea is broader than the probability alone field. Thus, the Wiener-Shannon's axioms can be extended to non-probabilistic events and it is possible to introduce a theory of information for non-repetitive events as a measure of the reliability of data for complex mechanical systems. To this end, one can devise engineering solutions consistent with the values of the design constraints analyzing the complexity of the relation matrix and using the idea of information in the metric space. The final solution gives the entropic measure of epistemic uncertainties which can be used in multibody system models, analyzed with an axiomatic design. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate and discuss the properties and characterizations of soft semi-Ti and soft semi-Di(for i = 0; 1; 2) spaces at soft point by analyzing the relationship among them. We also introduce and explore the properties of soft S-continuous functions. These results will be useful to enhance the theoretical framework and to promote further study towards the daily life applications. [ABSTRACT FROM AUTHOR]

Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Ésik. Models of these axioms include both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. We show that the standard result on the satisfaction of all Conway axioms by a unique dagger operation generalizes to the guarded setting. We also introduce the notion of guarded trace operator on a category, and we prove that guarded trace and guarded fixpoint operators are in one-to-one correspondence. Our results are intended as first steps leading, hopefully, towards future description of classifying theories for guarded recursion. [ABSTRACT FROM AUTHOR]

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, the status of reflection principles as axioms is left open for the Zermelian. [ABSTRACT FROM AUTHOR]

In this paper, the concept of fuzzy share functions of cooperative fuzzy games with fuzzy characteristic functions is proposed. Players in the proposed cooperative fuzzy game do not need to know precise information about the payoff value. We generalize the axiom of additivity by introducing a positive fuzzy value function ∼μ on the class of cooperative fuzzy games in fuzzy characteristic function form. The so-called axiom of ∼μ-additivity generalizes the classical axiom of additivity by putting the weight ∼μ(∼υ) on the value of the game ∼υ. We show that any additive function ∼μ- determines a unique fuzzy share function satisfying the axioms of effcient shares, null player property, symmetry and ∼μ-additivity on the subclass of games on which ∼μ is positive and which contains all positively scaled unanimity games. Finally, we introduce the fuzzy Shapley share functions and fuzzy Banzhaf share functions for the cooperative fuzzy games with fuzzy characteristic functions. [ABSTRACT FROM AUTHOR]

Based on the Zermelo-Fraenkel system of axioms ZF, we introduce a theory of essential closures. It is a generalization of the concept of topological closures in which a set may not be contained in its essential closure. A typical essential closure collects all points that are essential with respect to a submeasure; hence it is called a submeasure closure. One of our main results states that a "nice" essential closure must be a submeasure closure. Many examples of known and new submeasure closures are discussed and their applications are demonstrated, especially in the study of the supports of measures. [ABSTRACT FROM AUTHOR]

The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concepts of several separation axioms between the T0 and T1 spaces. We also characterize the modules such as the pm-module, m-module, ε-module, ES-module, D-module and Y-module. Some new results of the prime spectrum of a module M over a commutative ring R are given. [ABSTRACT FROM AUTHOR]

We study model companions of theories extending the graph axioms. First we prove general results concerning the existence of the model companion. Then, by applying these results to the case of graphs, we give a series of companionable and non-companionable examples. [ABSTRACT FROM AUTHOR]

In the new framework of the extended Fraenkel-Mostowski set theory, we define an extended interchange function as an action on a permutation group, and a new notion of permutative renaming by generalizing an existing notion of finitary permutative renaming. Some algebraic and combinatorial properties of permutative renamings expressed by using the Fraenkel-Mostowski axioms remain valid in the new framework even if we replace one axiom with a weaker axiom. [ABSTRACT FROM AUTHOR]

Among a group of selfish agents, we consider nomination correspondences that determine who should get a prize on the basis of each agent's nomination. Holzman and Moulin (Econometrica 81:173-196, ) show that (i) there is no nomination function that satisfies the axioms of impartiality, positive unanimity, and negative unanimity, and (ii) any impartial nomination function that satisfies the axiom of anonymous ballots is constant (and thus violates positive unanimity). In this article, we show that $$(\mathrm {i})^\prime $$ there exists a nomination correspondence, named plurality with runners-up, that satisfies impartiality, positive unanimity, and negative unanimity, and $$(\mathrm {ii})^\prime $$ any impartial nomination correspondence that satisfies anonymous ballots is not necessarily constant, but violates positive unanimity. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of fuzzy pre-open(fuzzy pre-closed) sets to introduce some new types of fuzzy pre-separation axioms (FPRi space) (for i = 0, 1)stronger forms of fuzzy pre-regular (fuzzy pre-normal) space are introduced and the relationship between these separation axioms and other are investigated. [ABSTRACT FROM AUTHOR]

In this paper, under the idea of L-T0 or sub-T0, we propose a set of new separation axioms in L-topological spaces, namely sub-separation axioms. And some of their properties are studied. In addition, the relation between the sub-separation axioms defined in the paper and other separation axioms is discussed. The results show that the subseparation axioms in this paper are weaker than other separation axioms that had appeared in literature. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule. [ABSTRACT FROM AUTHOR]

Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it into a particular form. [ABSTRACT FROM AUTHOR]

Abstract: A mean proximity rule is a voting rule having a mean proximity representation in Euclidean space. Legal ballots are represented as vectors that form the representing polytope. An output plot function determines a location for each possible election output in the same space, and these locations decompose the polytope into proximity regions according to which output is closest. The election outcome is then determined by which region(s) contain the mean position of all ballots cast. Mean neat rules are obtained by relaxing the requirement that the regions be determined by proximity, insisting only that they be neatly separable by a hyperplane. If each of these hyperplanes contains a dense set of rational points (vectors with all rational components), the mean neat voting rule is said to be rational . The aim of this article is to prove that consistency and connectedness are necessary and sufficient conditions for mean neat rationality of any voting rule that is anonymous . Connectedness can be viewed as a strong form of continuity, with an intuitive content related to the Intermediate Value Theorem (or to a discrete analogue of this theorem). The proof relies on a recent result in convexity theory [D. Cervone, W.S. Zwicker, Convex decompositions, J. Convex Anal. 2008 (in press)] and suggests a conjecture: if we relax connectedness to continuity, the class so characterized is that of the mean neat voting rules. This latter class properly contains all intuitive scoring rules. [Copyright &y& Elsevier]

We propose a local method of constructing piecewise G 1 Bézier patches to span a Bézier curve network with odd- and 4-valent node points. We analyze all possible singular cases of the G 1 condition that is to be met by the curve network interpolation and propose a new G 1 continuity condition using linear and quartic scalar weight functions. Using this condition, a curve network can be interpolated without modification at 4-valent nodes with two collinear tangent vectors, even in the presence of singularities. We demonstrate our approach by generating G 1 surfaces over the curve network which includes singularities at its node vertices and edges. [ABSTRACT FROM AUTHOR]

We shall introduce the notions of Λsp-closed and spg-closed sets. We also investigate properties of these sets and introduce some related new separation axioms. [ABSTRACT FROM AUTHOR]

The article presents a thesis discussing the fundamental theorem of projective geometry, which states that a semilinear transformation induces every line-preserving bijection of a Desaguersian projective plane. It is stated that the theorem extends to higher-dimensional projective spaces, affine transformations and even to buildings, which are combinatorial constructions. It considers the spaces' bijections preserving their geometry such as the transformations of quasi-spheres and proves local versions of theorems on arbitrary nondiscrete fields. Details on the parts of the thesis, which include a review of the theorem, nondiscrete topological fields and hypotheses involving measurable sets, are presented.