On sets of first-order formulas axiomatizing representable relation algebras

TL;DR

This thesis explores the foundational properties of representable relation algebras, establishing key results about their axiomatization, variety status, and basis complexity, with an elementary proof of Birkoff's variety theorem.

Contribution

It provides new proofs and comprehensive background on axiomatizing representable relation algebras, including demonstrating their non-finite basis and variable requirements.

Findings

RRA is a variety

RRA is not finitely based

Any equational basis for RRA has infinitely many variables

Abstract

This is the author's 2004 Master's thesis at Iowa State University, done under the supervision of Roger D. Maddux. It provides a background in relation algebras. Three results from the literature are demonstrated in full: (i.) RRA is a variety. (ii.) RRA is not finitely based. (iii.) Any equational basis for RRA has infinitely many variables. We also give an elementary proof of Birkoff's variety theorem.