Seminars & Colloquia Calendar

Logic Seminar

"Strong Chang's Conjecture and semiproperness of nonreasonable posets "

Sean Cox , Virginia Commonwealth University

Location:  HILL 705
Date & time: Monday, 01 May 2017 at 5:00PM -

 Abstract: A well-known theorem of Shelah states that semiproperness of Namba forcing is equivalent to a version of Strong Chang's Conjecture. We consider a certain poset $$mathbb{Q}$$ that: preserves stationary subsets of $$omega_1$$ and kills the stationarity of the ground model's $$[omega_2]^omega$$ (like Namba forcing); yet preserves that $$omega_2$$ has uncountable cofinality (unlike Namba forcing). We prove that semiproperness of $$mathbb{Q}$$ lies between two versions of Strong Chang's Conjecture (answering a question of Friedman-Krueger).

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