On regular reduced products
Juliette Cara Kennedy, Saharon Shelah · arXiv (Cornell University) · 2001
Assume ->. Assume M is a model of a first order theory T of cardinality at most lambda^+ in a vocabulary L(T) of cardinality holds. We show that then the second player has a winning strategy in the Ehrenfeucht-Fraisse game of length lambda^+ on prod_i M_i/D and prod_i N_i/D. This yields the following corollary: Assume GCH and lambda regular). For L, M_i and N_i as above, if D is a regular filter on lambda, then prod_i M_i/D cong prod_i N_i/D .