• Corpus ID: 237347066

Mutually embeddable models of ZFC

  title={Mutually embeddable models of ZFC},
  author={Monroe Eskew and Sy-David Friedman and Yair Hayut and Farmer Schlutzenberg},
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… 



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Large cardinals and definable well-orders on the universe

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.

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