منابع مشابه
Beppo Levi and the Arithmetic of Elliptic Curves T
Most students of mathematics encounter the name of the Italian mathematician Beppo Levi in integration theory when they learn "Beppo Levi's Lemma" on integrals of monotone sequences of functions. The attribution of this result is historically correct, but it by no means exhausts Beppo Levi's mathematical accomplishments. Between 1897 and 1909, Beppo Levi (1875-1961) actively participated in all...
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We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
متن کاملThe Axiom of Choice
We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
متن کاملUnions and the axiom of choice
Omar De la Cruz∗1, Eric J. Hall∗∗2, Paul Howard∗∗∗3, Kyriakos Keremedis†4, and Jean E. Rubin 1 Department of Statistics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA 2 Department of Mathematics and Statistics, University of Missouri, Kansas City, MO 64110, USA 3 Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA 4 Department of Mathemati...
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Luce’s choice axiom (LCA) is a theory of individual choice behavior that has proven to be a powerful tool in the behavioral sciences for over 50 years. LCA is grounded in two fundamental properties: choice is probabilistic and the probability of choosing an option from one set of alternatives is related to the probability of choosing the same option from a different set. This entry reviews the ...
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1979
ISSN: 0315-0860
DOI: 10.1016/0315-0860(79)90104-6