Jonsson-like partition relations and j: V → V

Autor:	Arthur W. Apter, Grigor Sargsyan
Rok vydání:	2004
Předmět:	Discrete mathematics elementary embeddings Jonsson cardinals Logic Elementary equivalence polarized partitions Combinatorics Mathematics::Logic 03E02 03E35 Philosophy 03E65 Corollary 03E55 partition relations Exponent Partition (number theory) Axiom of choice Axiom Mathematics
Zdroj:	J. Symbolic Logic 69, iss. 4 (2004), 1267-1281
ISSN:	1943-5886 0022-4812
DOI:	10.2178/jsl/1102022223
Popis:	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 . 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c26194fd9fe1107501d6a61d8c06a56 https://doi.org/10.2178/jsl/1102022223 Zobrazit plný text záznamu