The least strongly compact can be the least strong and indestructible

doi:10.1016/j.apal.2006.05.002

Annals of Pure and Applied Logic

Volume 144, Issues 1–3, December 2006, Pages 33-42

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Abstract

We construct two models in which the least strongly compact cardinal $κ$ is also the least strong cardinal. In each of these models, $κ$ satisfies indestructibility properties for both its strong compactness and strongness.

Keywords

Supercompact cardinal

Strongly compact cardinal

Strong cardinal

Indestructibility

Prikry forcing

Radin forcing

Closure point

Non-reflecting stationary set of ordinals

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^☆: The contents of this paper were presented in a lecture given at the January 20–26, 2002 meeting in Set Theory held at the Mathematics Research Institute, Oberwolfach, Germany. The author wishes to thank the organizers for having invited him to speak at and participate in a very stimulating conference.

¹: The author is pleased to offer this paper as his contribution to the special volume of Annals of Pure and Applied Logic being compiled in honor of the 60th birthday of Professor James Baumgartner of Dartmouth College. As is true with so many people, Jim’s encouragement and support have been invaluable over the years and have enriched both the mathematical and personal lives of those fortunate enough to know him.

Annals of Pure and Applied Logic

The least strongly compact can be the least strong and indestructible☆

Abstract

Keywords