Search 205,610,270 papers from all fields of science

Search

Sign InCreate Free Account

Corpus ID: 237347066

Mutually embeddable models of ZFC

@inproceedings{Eskew2021MutuallyEM,
title={Mutually embeddable models of ZFC},
author={Monroe Eskew and Sy-David Friedman and Yair Hayut and Farmer Schlutzenberg},
year={2021}
}

We investigate systems of transitive models of ZFC which are elementarily embeddable into each other and the influence of definability properties on such systems. One of Ken Kunen’s best-known and most striking results is that there is no elementary embedding of the universe of sets into itself other than the identity. Kunen’s result is best understood in a theory that includes proper classes as genuine objects, such as von Neumann-Gödel-Bernays set theory (NBG), which we take in this article… Expand

This article treats all cases by a uniform argument, starting with only one measurable cardinal and applying a cofinality-preserving forcing, and explores the possibilities for the number of normal measures on a cardinal at which the GCH fails.Expand

A reverse Easton forcing iteration is used to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals, by choosing the cardinals at which coding occurs sufficiently sparsely.Expand

We extend prior results of Cody-Eskew, showing the consistency of GCH with the statement that for all regular cardinals $\kappa \leq \lambda$, where $\kappa$ is the successor of a regular cardinal,… Expand