Dissertation/Thesis Abstract

A formalization of logic in diagonal-free cylindric algebras
by Ylvisaker, Andrew John, Ph.D., Iowa State University, 2012, 62; 3511508
Abstract (Summary)

We exhibit a quasi-projectional relation algebra reduct of any diagonal-free cylindric algebra of dimension 3 having sufficiently strong projection and equality parameters. We also offer a complete proof that full first-order logic can be formalized in the calculus of binary relations (a result due to Maddux and Tarski). Finally, we use these constructions to recursively define a translation function from the sentences of first-order logic to the equational theory of diagonal-free cylindric algebras of dimension 3 which preserves validity.

Indexing (document details)
Advisor: Maddux, Roger D.
Commitee: Axenovich, Maria, Bergman, Clifford, Robinson, William S., Sacks, Paul
School: Iowa State University
Department: Mathematics
School Location: United States -- Iowa
Source: DAI-B 73/10(E), Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Algebraic logic, Cylindric algebra, Diagonal-free, Relation algebra
Publication Number: 3511508
ISBN: 978-1-267-39349-4
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