NDLI: REALIZABILITY FOR CONSTRUCTIVE ZERMELO-FRAENKEL SET THEORY

Content Provider	Scilit
Author	Rathjen, Michael
Copyright Year	2006
Description	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, though, is concerned with a rather different interpretation. It is shown that Kleene realizability provides a self-validating semantics for CZF, viz. this notion of realizability can be formalized in CZF and demonstrably in CZF it can be verified that every theorem of CZF is realized. Book Name: Logic Colloquium '03
Related Links	https://content.taylorfrancis.com/books/download?dac=C2010-0-47466-9&isbn=9780367807092&doi=10.1201/9781439865835-14&format=pdf
Ending Page	314
Page Count	33
Starting Page	282
DOI	10.1201/9781439865835-14
Language	English
Publisher	Informa UK Limited
Publisher Date	2006-02-21
Access Restriction	Open
Subject Keyword	Book Name: Logic Colloquium '03 Realizability Constructive Zermelo Zermelo Fraenkel Fraenkel Set Set Theory Mathematics
Content Type	Text
Resource Type	Chapter

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