Consistency of V = HOD with the wholeness axiom
نویسندگان
چکیده
منابع مشابه
Consistency of V = HOD with the wholeness axiom
The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language {∈, j}, and that asserts the existence of a nontrivial elementary embedding j : V → V . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC+ V = HOD+ WA is consistent relative to the existence ...
متن کاملThe Wholeness Axioms and V=HOD
If the Wholeness Axiom WA0 is itself consistent, then it is consistent with v=hod. A consequence of the proof is that the various Wholeness Axioms are not all equivalent. Additionally, the theory zfc+wa0 is finitely axiomatizable. The Wholeness Axioms, proposed by Paul Corazza, occupy a high place in the upper stratosphere of the large cardinal hierarchy. They are intended as weakenings of the ...
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We construct two models showing the relative consistency of V = HOD with the level by level equivalence between strong compactness and supercompactness. In the first model, various versions of the combinatorial principles and ♦ hold. In the second model, the Ground Axiom (GA) holds.
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متن کاملHod, V and the GCH
Starting from large cardinals we construct a model of ZFC in which the GCH fails everywhere, but such that GCH holds in its HOD. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model of ZFC +GCH such that GCH fails everywhere in its HOD.
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2000
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s001530050144