324 citations · 1.7k across the 753 of their papers we have counts for
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More on the Ehrenfencht-Fraisse game of length omega_1
Tapani Hyttinen, Saharon Shelah, Jouko Väänänen
Let A and B be two first order structures of the same relational vocabulary L. The Ehrenfeucht-Fraisse-game of length gamma of A and B denoted by EFG_gamma(A,B) is defined as follo…
Possible Cardinalities of Maximal Abelian Subgroups of Quotients of Permutation Groups of the Integers
Saharon Shelah, Juris Stepráns
The maximality of Abelian subgroups play a role in various parts of group theory. For example, Mycielski has extended a classical result of Lie groups and shown that a maximal Abel…
Finite subgraphs of uncountably chromatic graphs
Péter Komjáth, Saharon Shelah
It is consistent that for every monotonically increasing function f:omega->omega there is a graph with size and chromatic number aleph_1 in which every n-chromatic subgraph has at…
Almost free groups and Ehrenfeucht-Fra\"ıssé games for successors of singular cardinals
Saharon Shelah, Pauli Väisänen
We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fraisse games between a fixed group of cardinality lambda and a free Abelian group.…
Games with creatures
Saharon Shelah, Jindrich Zapletal
Many forcing notions obtained using the creature technology are naturally connected with certain integer games.
Duality and the pcf theory
Saharon Shelah, Jindrich Zapletal
We consider natural cardinal invariants hm_n and prove several duality theorems, saying roughly: if I is a suitably definable ideal and provably cov(I)>=hm_n, then non(I) is provab…