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Relation algebras containing Thompson groups
Roger D. Maddux
The connections between Tarski's relation algebras and Thompson's groups F, T, V, and his monoid M are reviewed here, along with Jonsson-Tarski algebras, fork algebras, true pairin…
Tarskian classical relevant logic
Roger D. Maddux
The Tarskian classical relevant logic TR arises from Tarski's work on the foundations of the calculus of relations and on first-order logic restricted to finitely many variables, p…
Tarski's relevance logic; Version 2
Roger D. Maddux
Tarski's relevance logic is defined and shown to contain many formulas and derived rules of inference. The definition arises from Tarski's work on first-order logic restricted to f…
Canonical Relativized Cylindric Set Algebras and Weak Associativity
Roger D. Maddux
Canonical relativized cylindric set algebras are used to sharpen the relative representation theorem for weakly associative relation algebras, that every complete atomic weakly ass…
Relation algebras of Sugihara, Belnap, Meyer, and Church
Richard L. Kramer, Roger D. Maddux
Algebras introduced by, or attributed to, Sugihara, Belnap, Meyer, and Church are representable as algebras of binary relations with set-theoretically defined operations. They are…
Finite representations for two small relation algebras
Jeremy F. Alm, Roger D. Maddux
In this note, we give two different proofs that relation algebra is representable over a finite set. The first is probabilistic, and uses Johnson schemes. The second is a…
The finite representation property fails for composition and intersection
Roger D. Maddux
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
Subcompletions of representable relation algebras
Roger D. Maddux
Many finite symmetric integral non-representable relation algebras, including almost all Monk algebras, can be embedded in the completion of an atomic symmetric integral representa…
There is no finite-variable equational axiomatization of representable relation algebras over weakly representable relation algebras
Jeremy F. Alm, Robin Hirsch, Roger D. Maddux
We prove that any equational basis that defines RRA over wRRA must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable…