Authors: Kuzeljević, Boriša
Todorčević, Stevo 
Title: Forcing with matrices of countable elementary submodels
Journal: Proceedings of the American Mathematical Society
Volume: 145
Issue: 5
First page: 2211
Last page: 2222
Issue Date: 1-Jan-2017
Rank: M22
ISSN: 0002-9939
DOI: 10.1090/proc/13133
Abstract: 
We analyze the forcing notion P of finite matrices whose rows consist of isomorphic countable elementary submodels of a given structure of the form Hθ. We show that forcing with this poset adds a Kurepa tree T. Moreover, if Pc is a suborder of P containing only continuous matrices, then the Kurepa tree T is almost Souslin, i.e., the level set of any antichain in T is not stationary in ω1.
Keywords: Countable elementary submodel | Proper forcing | Side condition
Publisher: American Mathematical Society
Project: Set Theory, Model Theory and Set-Theoretic Topology 

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