Consistency of V = HOD with the wholeness axiom

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

The 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 ...

متن کامل

The Consistency of V = HOD with Level by Level Equivalence

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.

متن کامل

Indestructibility, HOD, and the Ground Axiom

Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, . . . , 4 are the theories “ZFC + φ1 + φ2”, “ZFC + ¬φ1 + φ2”, “ZFC + φ1 + ¬φ2”, and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, . . . , 4, Ai =df {δ < κ | δ is an inaccessible cardinal which is not a limit of inaccessible...

متن کامل

Hod, 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.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Archive for Mathematical Logic

سال: 2000

ISSN: 0933-5846,1432-0665

DOI: 10.1007/s001530050144