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Soluble omega-categorical groups

Published online by Cambridge University Press:  01 March 1997

RICHARD ARCHER  and
DUGALD MACPHERSON
RICHARD ARCHER
Affiliation:
19 Ommaney Rd., London, SE14 5NS
DUGALD MACPHERSON
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT
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Abstract

A countably infinite first-order structure M is ω-categorical if every countable N which has the same first-order theory as M is isomorphic to M. By a theorem due independently to Engeler[8], Ryll–Nardzewski[14] and Svenonius[19], this is equivalent to the condition that Aut M has finitely many orbits on Mn for all positive integers n. It is well known that ω-categorical algebraic structures are often intimately related to Boolean algebras. As examples, we mention Theorem 1·3, which is used later, and also the following theorem of J. S. Wilson (proved in [3]), which partly motivates our work.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 219 - 227
Copyright
© Cambridge Philosophical Society 1997

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