Nearly Model Complete Theories

✍ Scribed by David W. Kueker; Brian P. Turnquist

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 439 KB
• Volume: 45
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19990450302

✦ Synopsis

A theory T of a language L is 1-model complete (nearly model complete) iff for every formula p(5) of L there is a formula 8 ( 5 ) of L which is a V3-formula (a Boolean combination of universal formulas) such that T k VZ [p * 01. The main results of the paper give characterizations of nearly model complete theories and of l-model complete theories.

As a consequence we obtain that a theory T is nearly model complete iff whenever 93 is a model of T and U 23, then T U Ak is a complete L(A)-theory, where Ah is the 1-diagram of U. We also point out that our m a n results extend to (n + 1)-model complete and nearly n-model complete theories for all n > 0.