Series: Penn State Logic Seminar

Date: Tuesday, April 8, 2003

Time: 2:30 - 3:45 PM

Place: 113 McAllister Building

Speaker: Natasha Dobrinen, Penn State, Mathematics

Title:

A Complete Embedding of the cf$(2^{\omega})$-Cohen Algebra into the
Family of Galvin-Hajnal Algebras

Abstract:

We will give a Boolean algebraic construction of how to embed the
cf$(2^{\omega})$-Cohen algebra into each Galvin-Hajnal algebra as a
complete subalgebra.  This means that forcing with a Galvin-Hajnal
algebra adds cf$(2^{\omega})$-many side-by-side Cohen reals.  (We
thank the anonymous referee of a recent paper for pointing out that
our original proof that the Galvin-Hajnal algebra adds a Cohen real
actually proved this more general result.)  We will review the
relevant definitions and facts about complete embeddings of Boolean
algebras and give a detailed proof of the construction.