Vol. 94, No. 1, 1981

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ISSN: 0030-8730
The number of automorphisms of an atomic Boolean algebra

Judith Roitman

Vol. 94 (1981), No. 1, 231–242
Abstract

A method of construction via forcing is developed which allows great freedom in the interplay among the number of atoms, number of automorphisms, size of the algebra, and such objects of settheoretic interest as c. As by-products we have

Theorem 1. The following is consistent: there is a 0-dimensional Hausdorff space with fewer than c autohomeomorphisms, at least one of which moves a nonisolated point.

Theorem 2. The following is consistent: there is an infinite Boolean algebra with more automorphisms than elements, the number of whose automorphisms is not a power of 2.

Mathematical Subject Classification 2000
Primary: 03E35
Secondary: 06E99, 54H99
Milestones
Received: 3 October 1979
Revised: 26 June 1980
Published: 1 May 1981
Authors
Judith Roitman