Admissible Sets and Infinitary Logic

Abstract

Publisher Summary The relationship of admissible sets to logic can be summarized as the phenomenon that can be called the syntactic completeness of admissible sets. This chapter discusses admissible sets, the model theory of L ω1ω , classical descriptive set theory, effective descriptive set theory, and recursion theory. The main theme is the model theory of admissible fragments of L ω1ω . Further, the chapter features two recent devices: Vaught's use of conjunctive game sentences and Ressayre's ∑-saturated structures. The chapter presents examples of admissible sets and also discusses the Kripke–Platek axiom system Hintikka sets, model existence and Z-compactness, Conjunctive game formulas, and Z-saturated structures.