Rudimentary and arithmetical constructive set theory
نویسندگان
چکیده
منابع مشابه
Rudimentary and arithmetical constructive set theory
The CST conceptual framework is a set theoretical approach to constructive mathematics initiated by Myhill in [Myh75]. It has been given a philosophical foundation via formal interpretations into versions of Martin-Löf’s Intuitionistic Type Theory, [GA06, Acz86, Acz82, Acz78]. There are several axiom systems for Constructive Set Theory of varying logical strength. Perhaps the most familiar ones...
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4 Operations on Sets and Classes 25 4.1 Class Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Class Relations and Functions . . . . . . . . . . . . . . . . . . 26 4.3 Some Consequences of Union-Replacement . . . . . . . . . . . 27 4.4 Russell’s paradox . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 Subset Collection and Exponentiation . . . . . . . . . . . . . . 30...
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The paper furnishes realizability models of constructive Zermelo-Fraenkel set theory, CZF, which also validate Brouwerian principles such as the axiom of continuous choice (CC), the fan theorem (FT), and bar induction (BI), and thereby determines the proof-theoretic strength of CZF augmented by these principles. The upshot is that CZF+CC+FT possesses the same strength as CZF, or more precisely,...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.10.004