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Journal of Symbolic Logic, 1975
This paper is the third in a series collectively entitled Formal systems of intuitionistic analysis. The first two are [4] and [5] in the bibliography; in them I attempted to codify Brouwer's mathematical practice. In the present paper, which is independent of [4] and [5], I shall do the same for Bishop's book [1].
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This paper is the third in a series collectively entitled Formal systems of intuitionistic analysis. The first two are [4] and [5] in the bibliography; in them I attempted to codify Brouwer's mathematical practice. In the present paper, which is independent of [4] and [5], I shall do the same for Bishop's book [1].
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Elementary Constructive Operational Set Theory
2010We introduce a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set (in the sense of Aczel) with some aspects which are typical of Feferman's so-called "explicit mathematics".
CANTINI, ANDREA, L. Crosilla
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Constructive set theory with operations
2007We present an extension of Aczel's constructive Zermelo–Fraenkel set theory. Constructive sets are endowed with an applicative structure, which allows us to express several set theoretic constructs uniformly and explicitly. From the proof theoretic point of view, the addition is shown to be conservative.
CANTINI, ANDREA, L. Crosilla
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THE THEORY OF AFFINE CONSTRUCTIBLE SETS
Mathematical Logic Quarterly, 1983As it is well known, some problems of algebraic geometry can be translated into problems of pure algebra (by using the polynomials). But the polynomials also provide a primitive logic which describes structural features. The aim of this paper is to study constructible sets and the foundations of algebraic geometry from the point of view of the ...
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VERking in constructive set theory
ACM SIGSOFT Software Engineering Notes, 1981The constructive set theory of PL/CV3 is used to illustrate conditions that a formal system must satisfy if it is to feasibly represent the reasoning needed to solve sequential programming problems.
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Programming in Constructive Set Theory
Proceedings of the 1981 conference on Functional programming languages and computer architecture - FPCA '81, 1981@y e List(A) (Perm(x,y) & Sorted(y)) which is read “for all lists x, there is a sorted permutation y of x”. We can prove that this proposition is true, using the rules of the language to construct a program for the task. If the proposition were not true, it would be impossible to find a program for it and we would have had an impossible task. The types
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1985
There are two obvious approaches to constructive set theory: (i) Carefully add some set variables to a simpler theory, cautiously add some axioms about them, and try to explain the constructive meaning of the theory, (ii) Start with classical set theory, throw out the law of the excluded middle and any axioms which imply it, and see what is left over ...
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There are two obvious approaches to constructive set theory: (i) Carefully add some set variables to a simpler theory, cautiously add some axioms about them, and try to explain the constructive meaning of the theory, (ii) Start with classical set theory, throw out the law of the excluded middle and any axioms which imply it, and see what is left over ...
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Constructive Models of Set Theory
1985In this chapter we will present model constructions, or otherwise expressed, “concrete” realizability interpretations, for constructive set theories (sub-theories of intuitionistic ZF), patterned after the models of EM 0 and ML 1 given in preceding chapters.
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Homotopy theory of normed sets I. Basic constructions
St. Petersburg Mathematical Journal, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A constructive interpretation of the full set theory
The Journal of Symbolic Logic, 1987The interpretation of the ZF set theory reported in this paper is, actually, part of a wider effort, namely, a new approach to the foundation of mathematics, which is referred to as The Cybernetic Foundation. A detailed exposition of the Cybernetic Foundation will be published elsewhere.
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