منابع مشابه
Equivalents of the axiom of choice
Parts of this note have been discussed elsewhere in the blog, sometimes in a different form (see here and here, for example), but I haven’t examined before the equivalence of 5–7 with choice. In the course of the proof of the equivalence of item 7 with the other statements, a few additional equivalent versions of independent interest will be identified. The equivalence of 1–3 is classic. Zermel...
متن کاملReverse mathematics and equivalents of the axiom of choice
We study the reverse mathematics of countable analogues of several maximality principles that are equivalent to the axiom of choice in set theory. Among these are the principle asserting that every family of sets has a ⊆-maximal subfamily with the finite intersection property and the principle asserting that if φ is a property of finite character then every set has a ⊆-maximal subset of which φ...
متن کامل‘Regular’ Choice and the Weak Axiom of Stochastic Revealed Preference
We explore the relation between two 'rationality conditions' for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is...
متن کاملContextuality and the Weak Axiom in the Theory of Choice
Recent work on the logical structure of non-locality has constructed scenarios where observations of multi-partite systems cannot be adequately described by compositions of non-signaling subsystems. In this paper we apply these frameworks to economics. First we construct a empirical model of choice, where choices are understood as observable outcomes in a certain sense. An analysis of contextua...
متن کاملComputing with Sequences, Weak Topologies and the Axiom of Choice
We study computability on sequence spaces, as they are used in functional analysis. It is known that non-separable normed spaces cannot be admissibly represented on Turing machines. We prove that under the Axiom of Choice non-separable normed spaces cannot even be admissibly represented with respect to any compatible topology (a compatible topology is one which makes all bounded linear function...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1981
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093883463