April 4
Siiri Kivimäki,
University of Helsinki
Partitions and trees in Ehrenfeucht-Fraïssé games
We are interested in when are two uncountable models 'similar' - elementarily equivalent, elementarily equivalent in a stronger logic, or even isomorphic. Such equivalence is always characterized in terms of an Ehrenfeucht-Fraïssé game. We give two modifications of the standard Ehrenfeucht-Fraïssé game and discuss the logics these give rise to. The modified versions involve partitions of models and making the game longer using an Aronszajn tree as a game clock.