منابع مشابه
The 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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Let us consider two-sorted intuitionistic set theory ZFI2 with sort 0 for natural numbers and sort 1 for sets. We shall show that well-known Church rule with parameters of sort 1 is admissible in ZFI2 in some rather strong sense, and get from this point the admissibility of Markov rule with all parameters in ZFI2, and also DP and numerical EP with set parameters for it in the same sense.
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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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Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as L-fuzzy sets w.r.t. a special lattice L . Deschrijver [2] introduced additive and multiplicative generators on L based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on L as far as possible independ...
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Synopsis We give a general axiomatic construction of solutions to recursive domain equations, applicable both to classical models of domain theory and to realizability models. The approach is based on embedding categories of predomains in models of intuitionistic set theory. We show that the existence of solutions to recursive domain equations depends on the strength of the set theory. Such sol...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1972
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093890719