MoL-2012-11: An Ehrenfeucht-Fraisse Game for the Logic L-omega1-omega

MoL-2012-11: Wang, Tong (2012) An Ehrenfeucht-Fraisse Game for the Logic L-omega1-omega. [Report]

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The Ehrenfeucht-Fraïssé Game is very useful in studying separation and equivalence results in logic. The usual finite Ehrenfeucht-Fraïssé Game EFn characterizes separation in first order logic Lωω. The infinite Ehrenfeucht-Fraïssé Game EFω and the Dynamic Ehrenfeucht-Fraïssé Game EFDα characterize separation in L∞ω, the logic with arbitrary conjunctions and disjunctions of formulas. The logic Lω1 ω is the extension of first order logic with countable conjunctions and disjunctions of formulas. It is the most immediate, and perhaps the most important infinitary logic. However, there is no Ehrenfeucht-Fraïssé Game in the literature that characterizes separation in Lω1ω. In this thesis we introduce an Ehrenfeucht-Fraïssé Game for the logic Lω1ω . This game is based on a game for propositional and first order logic introduced by Hella and Väänänen. Unlike the usual Ehrenfeucht-Fraïssé Games which are modeled solely after the behavior of quantifiers, this new game also takes into account the behavior of boolean connectives in logic. We prove the adequacy theorem for this game. In the final part of the thesis we apply this game to prove complexity results about infinite binary strings.

Item Type: Report
Report Nr: MoL-2012-11
Series Name: Master of Logic Thesis (MoL) Series
Year: 2012
Uncontrolled Keywords: Logic, Mathematics
Depositing User: Tanja Kassenaar
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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