Splendid extensions

Shimon Garti

Splendid extensions

Logic 2026-07-09 v1

Authors: Shimon Garti

Abstract

Let $\kappa$ be a successor cardinal. We force a universe in which every model of PA of size $\kappa$ extends to a model M of the same size, where M has no splendid extensions. If there is an ineffable cardinal then this statement holds at some cardinal below it, in ZFC.

Cite

@article{arxiv.2607.08352,
  title  = {Splendid extensions},
  author = {Shimon Garti},
  journal= {arXiv preprint arXiv:2607.08352},
  year   = {2026}
}