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Cohen forcing and inner models
Author(s) -
Reitz Jonas
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201800062
Subject(s) - forcing (mathematics) , partially ordered set , cardinality (data modeling) , mathematics , combinatorics , discrete mathematics , pure mathematics , computer science , mathematical analysis , data mining
Given an inner model W ⊂ V and a regular cardinal κ, we consider two alternatives for adding a subset to κ by forcing: the Cohen poset Add(κ, 1), and the Cohen poset of the inner model Add ( κ , 1 ) W . The forcing from W will be at least as strong as the forcing from V (in the sense that forcing with the former adds a generic for the latter) if and only if the two posets have the same cardinality. On the other hand, a sufficient condition is established for the poset from V to fail to be as strong as that from W . The results are generalized to Add ( κ , λ ) , and to iterations of Cohen forcing where the poset at each stage comes from an arbitrary intermediate inner model.