Forcing with adequate sets of models as side conditions

Mathematical Logic Quarterly 63 (1-2):124-149 (2017)
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Abstract

We present a general framework for forcing on ω2 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 ω2, adding a nonreflecting stationary subset of, and adding an ω1‐Kurepa tree.

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10.1002/malq.201400022

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Citations of this work

Coherent adequate forcing and preserving CH.John Krueger & Miguel Angel Mota - 2015 - Journal of Mathematical Logic 15 (2):1550005.
Adding a club with finite conditions, Part II.John Krueger - 2015 - Archive for Mathematical Logic 54 (1-2):161-172.
Compactness versus hugeness at successor cardinals.Sean Cox & Monroe Eskew - 2022 - Journal of Mathematical Logic 23 (1).
Strongly adequate sets and adding a club with finite conditions.John Krueger - 2014 - Archive for Mathematical Logic 53 (1-2):119-136.
The approachability ideal without a maximal set.John Krueger - 2019 - Annals of Pure and Applied Logic 170 (3):297-382.

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References found in this work

Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Coherent adequate forcing and preserving CH.John Krueger & Miguel Angel Mota - 2015 - Journal of Mathematical Logic 15 (2):1550005.
Adding a club with finite conditions, Part II.John Krueger - 2015 - Archive for Mathematical Logic 54 (1-2):161-172.
Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
Forcing with finite conditions.Gregor Dolinar & Mirna Džamonja - 2013 - Annals of Pure and Applied Logic 164 (1):49-64.

View all 6 references / Add more references