منابع مشابه
The Tree Property at Both אω+1 and אω+2
We force from large cardinals a model of ZFC in which אω+1 and אω+2 both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model אω+2 even satisfies the super tree property.
متن کاملMore on full reflection below אω
Jech and Shelah [2] studied full reflection below אω, and produced a model in which the extent of full reflection is maximal in a certain sense. We produce a model in which full reflection is maximised in a different direction.
متن کاملThe Tree Property up to אω+1
Assuming ω supercompact cardinals we force to obtain a model where the tree property holds both at אω+1, and at אn for all 2 ≤ n < ω. A model with the former was obtained by Magidor–Shelah from a huge cardinal and ω supercompact cardinals above it, and recently by Sinapova from ω supercompact cardinals. A model with the latter was obtained by Cummings–Foreman from ω supercompact cardinals. Our ...
متن کاملDegree Bounds on Polynomials and Relativization Theory
We demonstrate the applicability of the polynomial degree bound technique to notions such as the nonexistence of Turing-hard sets in some relativized world, (non)uniform gap-definability, and relativized separations. This way, we settle certain open questions of Hemaspaandra, Ramachandran & Zimand [HRZ95] and Fenner, Fortnow & Kurtz [FFK94], extend results of Hemaspaandra, Jain & Vereshchagin [...
متن کاملA ZFC Dowker space in אω+1: an application of pcf theory to topology
The existence of an אω+1-Dowker space is proved in ZFC using pcf theory.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1983
ISSN: 0168-0072
DOI: 10.1016/0168-0072(83)90040-4