Publication
LICS 2021
Conference paper

Multi-Structural Games and Number of Quantifiers

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Abstract

We study multi-structural games, played on two sets \mathcal A and \mathcal B of structures. These games generalize Ehrenfeucht-Fraïssé games. Whereas Ehrenfeucht-Fraïssé games capture the quantifier rank of a first-order sentence, multi-structural games capture the number of quantifiers, in the sense that Spoiler wins the r-round game if and only if there is a first-order sentence φ with at most r quantifiers, where every structure in \mathcal A satisfies φ and no structure in \mathcal B satisfies φ. We use these games to give a complete characterization of the number of quantifiers required to distinguish linear orders of different sizes, and develop machinery for analyzing structures beyond linear orders.

Date

29 Jun 2021

Publication

LICS 2021

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