More canonical forms and dense free subsets

Annals of Pure and Applied Logic 125 (1-3):75-99 (2004)
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Abstract

Assuming the existence of ω compact cardinals in a model on GCH, we prove the consistency of some new canonization properties on ω. Our aim is to get as dense patterns in the distribution of indiscernibles as possible. We prove Theorem 2.1. thm2.1Suppose the consistency of “ZFC+GCH + there are infinitely many compact cardinals”. Then the following is consistent: ZFC+GCH + and for every family 0

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10.1016/j.apal.2003.10.001

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Citations of this work

The PCF Conjecture and Large Cardinals.Luís Pereira - 2008 - Journal of Symbolic Logic 73 (2):674 - 688.
Large cardinals and basic sequences.Jordi Lopez-Abad - 2013 - Annals of Pure and Applied Logic 164 (12):1390-1417.

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References found in this work

Some weak versions of large cardinal axioms.Keith J. Devlin - 1973 - Annals of Mathematical Logic 5 (4):291.
The consistency strength of the free-subset property for ωω.Peter Koepke - 1984 - Journal of Symbolic Logic 49 (4):1198 - 1204.
Some applications of short core models.Peter Koepke - 1988 - Annals of Pure and Applied Logic 37 (2):179-204.
Canonization theorems and applications.Saharon Shelah - 1981 - Journal of Symbolic Logic 46 (2):345-353.

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