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Graduate Operated Set Theory Seminar

"Cicho?'s Diagram" [Part 1]

Brian Pinsky

Location:  Canvas (really Big Blue Button)
Date & time: Wednesday, 08 April 2020 at 12:00PM - 1:00PM

Abstract: Cicho?'s diagram is a partial order describing the ZFC-provable relationships between 10 cardinal invariants of the continuum, relating null sets, comeager sets, and the bounding and dominating numbers. A classical set theory problem, completed in 1999, was to prove that Cicho?'s diagram completely describes these cardinals; i.e., for any not-obviously-inconsistent assignment of invariants to ?1 and ?2, constructing a model with those as the cardinaliites. In this talk, we will prove the relationships in Cicho?'s diagram. If time permits, we'll also start describing some forcings used to show the inequalities can be strict; although that will be our main topic next time.

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