Forcing with adequate sets of models as side conditions | Zendy

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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.

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