Semigroups, Horn sentences and isolic structures

Erik Maurice Ellentuck

Vol. 61 (1975), No. 1, 87–101

DOI: 10.2140/pjm.1975.61.87

Abstract

We introduce a special type of semigroup whose properties are abstracted from the theory of cardinal numbers under addition. A very general theorem about the behavior of universal Horn sentences in such semigroups is obtained and then applied to isols, recursive equivalence types, cardinal numbers, and Dedekind cardinals, the last two being in set theory without the axiom of choice.

Mathematical Subject Classification 2000

Primary: 02F40, 02F40

Secondary: 20M10, 04A10

Milestones

Received: 27 August 1974

Published: 1 November 1975