Set theoretical analogues of the Barwise-Schlipf theorem

Ali Enayat

Set theoretical analogues of the Barwise-Schlipf theorem

Logic 2022-06-27 v5

Authors: Ali Enayat

Abstract

We characterize nonstandard models of ZF (of arbitrary cardinality) that can be expanded to Goedel-Bernays class theory plus $\Delta^1_1$ -Comprehension. We also characterize countable nonstandard models of ZFC that can be expanded to Goedel-Bernays class theory plus $\Sigma^1_1$ -Choice.

Keywords

nonstandard models zf zfc goedel-bernays class theory delta-1-1 comprehension sigma-1-1 choice set theory

Cite

@article{arxiv.2001.09243,
  title  = {Set theoretical analogues of the Barwise-Schlipf theorem},
  author = {Ali Enayat},
  journal= {arXiv preprint arXiv:2001.09243},
  year   = {2022}
}

Comments

16 pages. This is the final version of the paper, and corrects some minor typos in the previous draft. The preliminaries section of the paper has a substantial text overlap with arXiv:1910.04029

Set theoretical analogues of the Barwise-Schlipf theorem

Abstract

Keywords

Cite

Comments

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