منابع مشابه
Axiom of Choice, Maximal Independent Sets, Argumentation and Dialogue Games
In this work we investigate infinite structures. We discuss the importance, meaning and temptation of the axiom of choice and equivalent formulations with respect to graph theory, abstract argumentation and dialogue games. Emphasis is put on maximal independent sets in graph theory as well as preferred semantics in abstract argumentation. 1998 ACM Subject Classification G.2.2 Graph Theory, F.4....
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This tutorial deals with the application of the Axiom of Choice in one of its popular disguises to objects which are of some interest in computer science (like lattices, Boolean algebras, filters and ideals, games). We discuss some common variants of this axiom such as Zorn's Lemma, Tuckey's Maximality Principle, the Well-Ordering Theorem and the Maximal Ideal Theorem; each equivalence gives ap...
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The discussion of cardinalities in Chapter 2 suggests that the most interesting thing about them is their order relation, namely that any set of cardinalities forms a well-ordered set. So in this section we shall embark upon a systematic study of well-ordered sets. Remarkably, we will see that the problem of classifying sets up to bijection is literally contained in the problem of classifying w...
متن کاملUniform Eberlein Spaces and the Finite Axiom of Choice
We work in set-theory without choice ZF. Given a closed subset F of [0, 1] which is a bounded subset of l(I) (resp. such that F ⊆ l(I)), we show that the countable axiom of choice for finite subsets of I, (resp. the countable axiom of choiceACN) implies that F is compact. This enhances previous results where ACN (resp. the axiom of Dependent Choices DC) was required. Moreover, if I is linearly ...
متن کاملEnvelope Theorems For Finite Choice Sets
This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and for each alternative, the objective function...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1945
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-33-1-137-168