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A simple tree lemma and its application to a counterexample of philips

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Abstract

We prove a tree lemma on perfect trees to obtain an ultrafilter of definable subsets of ℕ, which is Ramsey but not conservative (see [Phi 2]).

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References

  1. Blass, A.: On certain types and models of arithmetic. JSL39, 151–162 (....).

  2. Phillips, R. G.: Omitting types in arithmetic and conservative extensions. Proc. of the Victoria Symp. on Non Standard Analysis, Lect. Notes in Math. Nr., pp. 195–202. Berlin, Heidelberg, New York 1974.

  3. Phillips, R. G.: A minimal extension that is not conservative. Mich. Math. J. vol.21, 27–32 (1974).

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Authors
  1. Klaus Potthoff
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Potthoff, K. A simple tree lemma and its application to a counterexample of philips. Arch math Logik 18, 67–71 (1977). https://doi.org/10.1007/BF02007258

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  • DOI: https://doi.org/10.1007/BF02007258

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