Abstract

It is a wel known fact that the finite products of Hintikka-Fraissé types for sentences of quantifier rank n give rise to the set of atoms of a finite boolean algebra. In this paper we consider the class of (Lww)t-types introduced in [4], which caracterizes in a pure topological way the (Lww)t-equivalence for T3 spaces. We define for every nonempty family I of n-types a product xInai in such a way that if I is a family of T3 spaces, XIAi denotes its product with the box topology and (ai)1ε XIAi we have that if the n-type of ai is ai (i ε I), then the n-type of (ai)I is xInai. We then prove that, for every n ≥ 1, it is possible to define a lineal order nI of satisfiable n-types and every J c I, we have xJαj ≤nxlnαi. We also prove that these results for Ziegler’s typescan be generalized, if we consider the class of (Lω1ω)t-types introduced in [6], which permits to characterize the (Lω1ω)t-equivalence for a wide class of T3 spaces