The Fraenkel-Carnap question for Dedekind algebras

✍ Scribed by George Weaver; Benjamin George

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 103 KB
• Volume: 49
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200310008

✦ Synopsis

Abstract

It is shown that the second‐order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second‐order theory is categorical. It follows that the second‐order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second‐order theory of a Dedekind algebra is quasi‐finitely axiomatizable iff the algebra is quasi‐finitely characterizable.