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December 2004 Jonsson-like partition relations and j: V → V
Arthur W. Apter, Grigor Sargsyan
J. Symbolic Logic 69(4): 1267-1281 (December 2004). DOI: 10.2178/jsl/1102022223

Abstract

Working in the theory “ZF + There is a nontrivial elementary embedding j: V → V ”, we show that a final segment of cardinals satisfies certain square bracket finite and infinite exponent partition relations. As a corollary to this, we show that this final segment is composed of Jonsson cardinals. We then show how to force and bring this situation down to small alephs. A prototypical result is the construction of a model for ZF in which every cardinal μ ≥ ℵ2 satisfies the square bracket infinite exponent partition relation μ → [μ]ω2. We conclude with a discussion of some consistency questions concerning different versions of the axiom asserting the existence of a nontrivial elementary embedding j : V → V. By virtue of Kunen's celebrated inconsistency result, we use only a restricted amount of the Axiom of Choice.

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Arthur W. Apter. Grigor Sargsyan. "Jonsson-like partition relations and j: V → V." J. Symbolic Logic 69 (4) 1267 - 1281, December 2004. https://doi.org/10.2178/jsl/1102022223

Information

Published: December 2004
First available in Project Euclid: 2 December 2004

zbMATH: 1071.03029
MathSciNet: MR2135668
Digital Object Identifier: 10.2178/jsl/1102022223

Subjects:
Primary: 03E02, 03E35, 03E55, 03E65

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 4 • December 2004
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