Theories with a finite number of models in an uncountable power are categorical

Alistair H. Lachlan

Vol. 61 (1975), No. 2, 465–481

DOI: 10.2140/pjm.1975.61.465

Abstract

In this paper are considered complete, countable, first-order theories which have a finite number of models in some uncountable power. It is shown that any such theory is either ω-categorical or ω₁-categorical. This confirms a conjecture of W. K. Forrest.

Mathematical Subject Classification

Primary: 02H05, 02H05

Secondary: 02G20

Milestones

Received: 16 January 1975

Published: 1 December 1975