Collapsing the cardinals of HOD-Reference-Cited by-同舟云学术

Collapsing the cardinals of HOD

Published:2015-12 Issue:02 Volume:15 Page:1550007
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Cummings James¹,Friedman Sy David²,Golshani Mohammad³

Affiliation:

1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA

2. Kurt Gödel Research Center for Mathematical Logic, Währinger Strasse 25, 1090 Vienna, Austria

3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

Abstract

Assuming that GCH holds and [Formula: see text] is [Formula: see text]-supercompact, we construct a generic extension [Formula: see text] of [Formula: see text] in which [Formula: see text] remains strongly inaccessible and [Formula: see text] for every infinite cardinal [Formula: see text]. In particular the rank-initial segment [Formula: see text] is a model of ZFC in which [Formula: see text] for every infinite cardinal [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061315500075

Reference10 articles.

1. Homogeneous iteration and measure one covering relative to HOD

2. The Generalized Continuum Hypothesis Can Fail Everywhere

3. The fine structure of the constructible hierarchy

4. KWithout the Measurable

5. Radin forcing and its iterations

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4. On the powersets of singular cardinals in HOD;Proceedings of the American Mathematical Society;2020-01-13

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