Existentially Incomplete Tame Models and a Conjecture of Ellentuck |
| |
| Authors: | Thomas G McLaughlin |
| |
| Institution: | Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409, U.S.A. |
| |
| 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. |
| |
| Keywords: | Tame model Isol Regressive isol Semiring Existentially complete Torre model |
|
|
