Elementary extensions of models of set theory

@article{Schmerl2000ElementaryEO,
  title={Elementary extensions of models of set theory},
  author={James H. Schmerl},
  journal={Arch. Math. Log.},
  year={2000},
  volume={39},
  pages={509-514}
}
A theorem of Enayat’s concerning models of ZFC which had been proved using several different additional set-theoretical hypotheses is shown here to be absolute. Let A ≺ B be models ofZFC, and letκ ∈ A be such that A |= “κ is an ordinal ”. Then we say that B is aκ-elementary end extension (i brief: κe.e.e. ) if κ is the least ordinal of A such that for some b ∈ B\A,B |= b ε κ. A cardinalκ ismeasurableif there is a nonprincipal, κ-complete ultrafilter overκ. In particular, we consider ω to… CONTINUE READING

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