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Complexity of index sets of computable lattices

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Item Summary

Title:Complexity of index sets of computable lattices
Authors:Nguyen, Paul Kim Long Vu
Keywords:algebras
Date Issued:Aug 2014
Publisher:[Honolulu] : [University of Hawaii at Manoa], [August 2014]
Abstract:We analyze computable algebras in the sense of universal algebra and the index set complexity of properties of such algebras. We look at the difficulty of determining properties of Con(A), the congruence lattice of an algebra A. In particular, we introduce the notion of a class of algebras witnessing the complexity of a property of algebras and show that computable lattices witness the 02-completeness of being simple, as well as witnessing the 03-completeness of having finitely many congruences. Finally, in our main result, we show that the property "to be subdirectly irreducible" is 03-complete as well, and in the process show that computable lattices witness this.
Description:Ph.D. University of Hawaii at Manoa 2014.
Includes bibliographical references.
URI/DOI:http://hdl.handle.net/10125/100392
Rights:All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Appears in Collections: Ph.D. - Mathematics


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