Independence results around constructive ZF
نویسندگان
چکیده
منابع مشابه
Independence results around constructive ZF
When making the transition from a classical to an intuitionistic system, one is compelled to reconsider the axioms chosen. For instance, it would be natural to re-formulate those that imply Excluded Middle. In the context of set theory, typically the Axiom of Foundation is substituted by the Axiom of Set Induction, the two being equivalent classically but the latter not yielding Excluded Middle...
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We formalise the axiomatic set theory second-order ZF in the constructive type theory of Coq assuming excluded middle. In this setting we prove Zermelo’s embedding theorem for models, categoricity in all cardinalities, and the correspondence of inner models and Grothendieck universes. Our results are based on an inductive definition of the cumulative hierarchy eliminating the need for ordinals ...
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+'-1bl~-~~)~~-~~nlcinll minor corr(!clion~. changc!! and revisions to n prelimlnary IIlmrion which appcilrcd In the Proc. or the 12lh Annual ACM Symposium on the Theory of Compulirl,g (!.lilY 19110). P,lrl of the work reported here will appear in the first author's 1981 doctoral <Ij!i!lcrL"Lion to he wriUen nt Purdue Univr.rl1iLy under the direction of the second author.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2004.08.002