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Forcing with adequate sets of models as side conditions
Author(s) -
Krueger John
Publication year - 2017
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.201400022
Subject(s) - forcing (mathematics) , countable set , mathematics , type (biology) , function (biology) , tree (set theory) , pure mathematics , mathematical analysis , geology , evolutionary biology , biology , paleontology
We present a general framework for forcing on ω 2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω 2 , adding a nonreflecting stationary subset ofω 2 ∩ cof ( ω ) , and adding an ω 1 ‐Kurepa tree.