Pseudofinite fields, procyclic fields and model-completion

Allan Russell Adler and Catarina Isabel Kiefe

Vol. 62 (1976), No. 2, 305–309

DOI: 10.2140/pjm.1976.62.305

Abstract

In this paper, it is shown that the theory of pseudofinite fields is, with respect to a suitable language, the model completion of the theory of procyclic fields. Also, procyclic fields are characterized as the class of relatively algebraically closed subfields of pseudofinite fields.

Mathematical Subject Classification 2000

Primary: 02H15, 02H15

Secondary: 12L10

Milestones

Received: 1 January 1975

Published: 1 February 1976