Document Type
Article
Publication Date
12-2008
Abstract
We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yields isomorphism (elementary equivalence) of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable partial automorphisms.
Recommended Citation
Chubb, Jennifer; Harizanov, Valentina; Morozov, Andrei; Pingrey, Sarah; and Ufferman, Eric, "Partial Automorphism Semigroups" (2008). Mathematics. 3.
https://repository.usfca.edu/math/3
Comments
Preprint. Article published in Annals of Pure & Applied Logic December 2008, Vol. 156 Issue 2/3, p245-258, 14p. DOI:10.1016/j.apal.2008.06.016.