Infinitary logic and admissible sets

Abstract

In recent years much effort has gone into the study of languages which strengthen the classical first-order predicate calculus in various ways. This effort has been motivated by the desire to find a language which is

(I) strong enough to express interesting properties not expressible by the classical language, but

(II) still simple enough to yield interesting general results. Languages investigated include second-order logic, weak second-order logic, ω-logic, languages with generalized quantifiers, and infinitary logic.