Adding closed unbounded subsets of \(\omega_2\) with finite forcing

DOI10.1305/ndjfl/1125409334zbMath1095.03038OpenAlexW2010713684MaRDI QIDQ816296

William J. Mitchell

Publication date: 10 March 2006

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1305/ndjfl/1125409334

zbMATH Keywords

consistencyapproachability idealnonstationary idealMahlo cardinals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Ordered sets and their cofinalities; pcf theory (03E04)

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MITCHELL-INSPIRED FORCING, WITH SMALL WORKING PARTS AND COLLECTIONS OF MODELS OF UNIFORM SIZE AS SIDE CONDITIONS, AND GAP-ONE SIMPLIFIED MORASSES, Two applications of finite side conditions at \(\omega _2\), SPECIALISING TREES WITH SMALL APPROXIMATIONS I, Forcing with adequate sets of models as side conditions, Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties, Forcing with sequences of models of two types, Characterizing large cardinals through Neeman's pure side condition forcing, Fragility and indestructibility. II, Why Y-c.c., Guessing models and the approachability ideal, Almost strong properness, 𝐼[𝜔₂ can be the nonstationary ideal on 𝐶𝑜𝑓(𝜔₁)], Some problems in singular cardinals combinatorics

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