English

The first-order definability of generic large cardinals

Logic 2021-07-01 v2

Abstract

We show that the notions of generic and Laver-generic supercompactness are first-order definable in the language of ZFC. This also holds for generic and Laver-generic (almost) hugeness as well as for generic versions of other large cardinals.

Keywords

Cite

@article{arxiv.2106.14129,
  title  = {The first-order definability of generic large cardinals},
  author = {Sakaé Fuchino and Hiroshi Sakai},
  journal= {arXiv preprint arXiv:2106.14129},
  year   = {2021}
}