GAMES AND CARDINALITIES IN INQUISITIVE FIRST-ORDER LOGIC
Gianluca Grilletti, Ivano Ciardelli · The Review of Symbolic Logic · 2021
Abstract Inquisitive first-order logic,InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game forInqBQand show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what statements and questions can be expressed inInqBQabout the number of individuals satisfying a given predicate. As special cases, we show that several variants of the questionhow many individuals satisfy $\alpha (x)$ are not expressible inInqBQ, both in the general case and in restriction to finite models.