ON THE GENERAL INTERPRETATION OF FIRST-ORDER QUANTIFIERS

Abstract

AbstractWhile second-order quantifiers have long been known to admit nonstandard, or“general” interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretation’s first-order domain. This paper explores some of the consequences of such “general” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.