dc.creator | Smedberg, Matthew Raine | |
dc.date.accessioned | 2020-08-21T21:08:42Z | |
dc.date.available | 2014-04-04 | |
dc.date.issued | 2014-04-04 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-03132014-114415 | |
dc.identifier.uri | http://hdl.handle.net/1803/10752 | |
dc.description.abstract | We show that several kinds of local behavior in a finite algebra A present obstructions to the decidability of the first-order theory of the finite members of HSP(A). In particular, we show that every solvable congruence in a locally finite, finitely decidable variety is abelian, and that the subdirectly irreducible algebras in such a variety have very constrained congruence geometry, generalizing results of Idziak, Valeriote, and Willard for congruence-modular varieties. We then show that every finitely generated, finitely decidable variety is residually finite (indeed, has a finite residual bound). Finally we modify a construction of Valeriote to give a tighter bound on the essential arity of a sigma-sorted term operation of A. | |
dc.format.mimetype | application/pdf | |
dc.subject | strongly abelian | |
dc.subject | finite decidability | |
dc.subject | computability | |
dc.subject | locally finite varieties | |
dc.title | Necessary conditions for finite decidability in locally finite varieties admitting strongly abelian behavior | |
dc.type | dissertation | |
dc.contributor.committeeMember | Constantine Tsinakis | |
dc.contributor.committeeMember | Mark Sapir | |
dc.contributor.committeeMember | Denis Osin | |
dc.contributor.committeeMember | Miklos Maroti | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2014-04-04 | |
local.embargo.lift | 2014-04-04 | |
dc.contributor.committeeChair | Ralph McKenzie | |