منابع مشابه
Determinacy in third order arithmetic
In recent work, Schweber [7] introduces a framework for reverse mathematics in a third order setting and investigates several natural principles of transfinite recursion. The main result of that paper is a proof, using the method of forcing, that in the context of two-person perfect information games with moves in R, open determinacy (Σ1 -DET) is not implied by clopen determinacy (∆ R 1 -DET). ...
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We establish the precise bounds for the amount of determinacy provable in second order arithmetic. We show that for every natural number n, second order arithmetic can prove that determinacy holds for Boolean combinations of n many Π3 classes, but it cannot prove that all finite Boolean combinations of Π3 classes are determined. More specifically, we prove that Πn+2-CA0 ` n-Π3-DET, but that ∆n+...
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In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0, which consists of the axioms of discrete ordered semi-ring with exponentiation, ∆1 comprehension and Π 0 0 induction, and which is k...
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We investigate the reverse mathematical strength of Turing determinacy up to Σ5 which is itself not provable in second order arithmetic.
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We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the basic principles of conceptualism in a formal system CM set in the language of third order arithmetic. This paper is part of a project whose goal is to make a ca...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2017
ISSN: 0168-0072
DOI: 10.1016/j.apal.2017.05.004