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.
|Advisor:||Maddux, Roger D.|
|Commitee:||Axenovich, Maria, Bergman, Clifford, Robinson, William S., Sacks, Paul|
|School:||Iowa State University|
|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|
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