Vol. 61, No. 2, 1975

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ISSN: 0030-8730
Theories with a finite number of models in an uncountable power are categorical

Alistair H. Lachlan

Vol. 61 (1975), No. 2, 465–481
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
Authors
Alistair H. Lachlan