Typical ambiguity and elementary equivalence

✍ Scribed by Daniel Dzierzgowski

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 577 KB
• Volume: 39
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19930390147

✦ Synopsis

Abstract

A sentence of the usual language of set theory is said to be stratified if it is obtained by “erasing” type indices in a sentence of the language of Russell's Simple Theory of Types. In this paper we give an alternative presentation of a proof the ambiguity theorem stating that any provable stratified sentence has a stratified proof. To this end, we introduce a new set of ambiguity axioms, inspired by Fraïssé's characterization of elementary equivalence; these axioms can be naturally used to give different proofs of the ambiguity theorem (semantic or syntactic, classical or intuitionistic). MSC: 03B15, 03F50, 03F55.