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Constructive Set Theory with Operations
In Alessandro Andretta, Keith Kearnes & Domenico Zambella (eds.), Logic Colloquium 2004: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. Cambridge: Cambridge University Press (2007)
Abstract
We present an extension of constructive Zermelo{Fraenkel set theory [2]. 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. In particular, we single out a theory of constructive sets with operations which has the same strength as Peano arithmetic.Author Profiles
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Citations of this work
Set theory: Constructive and intuitionistic ZF.Laura Crosilla - 2010 - Stanford Encyclopedia of Philosophy.
Explicit mathematics and operational set theory: Some ontological comparisons.Gerhard Jäger & Rico Zumbrunnen - 2014 - Bulletin of Symbolic Logic 20 (3):275-292.
The axiom of choice and combinatory logic.Andrea Cantini - 2003 - Journal of Symbolic Logic 68 (4):1091-1108.
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