Annals of Pure and Applied Logic 60 (3):261-274 (1993)

We prove that if is a model of size at most [kappa], λ[kappa] = λ, and a game sentence of length 2λ is true in a 2λ-saturated model ≡ , then player has a winning strategy for a related game in some ultrapower ΠD of . The moves in the new game are taken in the cartesian power λA, and the ultrafilter D over λ must be chosen after the game is played. By taking advantage of the expressive power of game sentences, we obtain several applications showing the existence of ultrapowers with certain properties. In each case, it was previously known that such ultrapowers exist under the assumption of the GCH, and we get them without the GCH. Article O
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DOI 10.1016/0168-0072(93)90078-r
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References found in this work BETA

Some Applications of Infinitely Long Formulas.H. Jerome Keisler - 1965 - Journal of Symbolic Logic 30 (3):339-349.
The Isomorphism Property Versus the Special Model Axiom.Renling Jin - 1992 - Journal of Symbolic Logic 57 (3):975-987.

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Citations of this work BETA

The Strength of the Isomorphism Property.Renling Jin & Saharon Shelah - 1994 - Journal of Symbolic Logic 59 (1):292-301.
Type Two Cuts, Bad Cuts and Very Bad Cuts.Renling Jin - 1997 - Journal of Symbolic Logic 62 (4):1241-1252.

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