Existentially Incomplete Tame Models and a Conjecture of Ellentuck

Mathematical Logic Quarterly 45 (2):189-202 (1999)
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Abstract

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many do, some do not

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10.1002/malq.19990450204

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Sub-arithmetical ultrapowers: a survey.Thomas G. McLaughlin - 1990 - Annals of Pure and Applied Logic 49 (2):143-191.
Recursive ultrapowers, simple models, and cofinal extensions.T. G. McLaughlin - 1992 - Archive for Mathematical Logic 31 (4):287-296.
Torre models in the isols.Joseph Barback - 1994 - Journal of Symbolic Logic 59 (1):140-150.
Existentially Complete Nerode Semirings.Thomas G. McLaughlin - 1995 - Mathematical Logic Quarterly 41 (1):1-14.
Forcing, Arithmetic, Division Rings.Joram Hirschfeld & William H. Wheeler - 1980 - Journal of Symbolic Logic 45 (1):188-190.

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