In the context of arbitrary Polish groups, we investigate the Galvin– Mycielski–Solovay characterization of strong measure zero sets as those sets for which a meager collection of right translates cannot cover the

The local chromatic number of a graph was introduced in [13]. It is in between the chromatic and fractional chromatic numbers. This motivates the study of the local chromatic number of graphs for which these quantities are far apart. Such graphs include Kneser graphs, their vertex color-critical subgraphs, the stable Kneser (or Schrijver) graphs; Mycielski graphs, and their generalizations; and...

Let A and B be two first order structures of the same vocabulary. We shall consider the Ehrenfeucht-Fräıssé-game of length ω1 of A and B which we denote by Gω1(A,B). This game is like the ordinary Ehrenfeucht-Fräıssé-game of Lωω except that there are ω1 moves. It is clear that Gω1(A,B) is determined if A and B are of cardinality ≤ א1. We prove the following results:

Remark 0.1 (Preliminary version.) This is an extremely preliminary version of my paper for the Ann Arbor proceedings. It contains some material (e.g guide to reading 394) which will almost certainly come out. But it does provide I think some insight into Shelah’s use of Ehrenfeucht-Mostowski models which I hadn’t understood. Even more than usual comments on both the general direction and specif...

We study how equivalent nonisomorphic models of unsuperstable theories can be. We measure the equivalence by Ehrenfeucht-Fraisse games. This paper continues [HS].