Map Theory: From Well-Foundation to Antifoundation
نویسندگان
چکیده
منابع مشابه
Map Theory: From Well-Foundation to Antifoundation
Map Theory is a powerful extension of type-free lamba-calculus (with only a few term constants added). Due to Klaus Grue, it was designed to be a common foundation for Computer Sciences and for Mathematics. All the primitive notions of first-order logic and set theory, including truth values, connectives and quantifiers, set-membership and set-equality, are interpreted as terms. All the usual s...
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متن کاملErratum: "Forcing and antifoundation"
Sato Kentaro pointed out a serious flaw in the proof of the main result (Truth Lemma 3.15) of [1]. Namely the greatest fixed point, Φ∞, of the operator Φ in definition 3.12 is taken to be inside the model M , while Φ∞ in lemma 3.6 is actually constructed outside M . The two definitions need not be identical (at least I can’t prove that they are). So what lemma 3.15 of [1] actually proves is tha...
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متن کاملForcing and antifoundation
It is proved that the forcing apparatus can be built and set to work in ZFCA (=ZFC minus foundation plus the antifoundation axiom AFA). The key tools for this construction are greatest fixed points of continuous operators (a method sometimes referred to as “corecursion”). As an application it is shown that the generic extensions of standard models of ZFCA are models of ZFCA again.
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2004
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2004.08.010