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.