Extensional realizability for intuitionistic set theory
نویسندگان
چکیده
منابع مشابه
Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory
A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by V. Lifschitz in [15]. A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten [19]. In that paper he also extended Lifschitz’ realizability to second order arithmetic. The ...
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Constructive Zermelo-Fraenkel Set Theory, CZF, has emerged as a standard reference theory that relates to constructive predicative mathematics as ZFC relates to classical Cantorian mathematics. A hallmark of this theory is that it possesses a type-theoretic model. Aczel showed that it has a formulae-as-types interpretation in Martin-Löf’s intuitionist theory of types [14, 15]. This paper, thoug...
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Given a partial combinatory algebra (pca) A (see e.g. [16]) together with a subpca A# of A we will construct the nested realizability topos RT(A,A#) as described in [5] (without giving it a proper name there). It is well known (from e.g. [16]) that RT(A,A#) appears as the exact/regular completion of its subcategory Asm(A,A#) of assemblies. In [5] the authors considered two complementary subtopo...
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3 Recursive Realizability Interpretations 16 3.1 Abstract Applicative Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Realizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Soundness for IZF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Term Extraction . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملThe Intuitionistic Alternative Set Theory
Lano, K., The intuitionistic alternative set theory, Annals of Pure and Applied Logic 59 (1993) 141-156. The Alternative Set Theory, as defined in Vopenka and Sochor, demonstrates how a set theory which avoids actually infinite sets can serve as a framework for much of classical mathematics. This paper defines a theory which can serve as an intuitionistic analogue of AST, and examines motivatio...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2020
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exaa087