SUITABLE EXTENDER MODELS I-Reference-Cited by-同舟云学术

SUITABLE EXTENDER MODELS I

Published:2010-06 Issue:01n02 Volume:10 Page:101-339
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

WOODIN W. HUGH¹

Affiliation:

1. Department of Mathematics, University of California Berkeley, CA 94720, USA

Abstract

We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Gödel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central issue for the Inner Model Program.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021906131000095X

Reference19 articles.

1. Universally Baire Sets of Reals

2. Perspectives in Mathematical Logic;Kanamori A.,1994

3. The axiom of determinacy, strong partition properties and nonsingular measures

4. The Stationary Tower

5. Certain very large cardinals are not created in small forcing extensions

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