Jonsson-like partition relations and j: V → V
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 1267-1281 / Harvested from Project Euclid
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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]ωℵ2. 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.
Publié le : 2004-12-14
Classification:  Jonsson cardinals,  partition relations,  polarized partitions,  elementary embeddings,  03E02,  03E35,  03E55,  03E65 
@article{1102022223,
     author = {Apter, Arthur
W. and Sargsyan, Grigor},
     title = {Jonsson-like partition relations and j: V $\rightarrow$ V},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 1267-1281},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1102022223}
}

Apter, Arthur
W.; Sargsyan, Grigor. Jonsson-like partition relations and j: V → V. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  1267-1281. http://gdmltest.u-ga.fr/item/1102022223/