Separating club-guessing principles in the presence of fat forcing axioms

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• 作者：David Asperó ; ^a ; ^{d.aspero@uea.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Miguel Angel Mota^b ; ^{motagaytan@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：03E50 ; 03E57 ; 03E35 ; 03E05
• 刊名：Annals of Pure and Applied Logic
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：167
• 期：3
• 页码：284-308
• 全文大小：624 K

文摘

We separate various weak forms of Club Guessing at ω₁${\omega }_1$ in the presence of 2^ℵ₀$2^{{\mathrm{\aleph }}_0}$ large, Martin's Axiom, and related forcing axioms.

We also answer a question of Abraham and Cummings concerning the consistency of the failure of a certain polychromatic Ramsey statement together with the continuum large.

030">All these models are generic extensions via finite support iterations with symmetric systems of structures as side conditions, possibly enhanced with ω-sequences of predicates, and in which the iterands are taken from a relatively small class of forcing notions.

We also prove that the natural forcing for adding a large symmetric system of structures (the first member in all our iterations) adds ℵ₁${\mathrm{\aleph }}_1$-many reals but preserves CH.