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  1. Existentially Incomplete Tame Models and a Conjecture of Ellentuck.Thomas G. McLaughlin - 1999 - Mathematical Logic Quarterly 45 (2):189-202.
    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 (...)
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