Bjarni J'onsson and Alfred Tarski, Representation problems for relation algebras, Abstract 89, Bulletin of the American Mathematical Society 54 (1948), 80 and 1192.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Part of the reason for this is obvious: a relation algebra is a Boolean algebra with additional operators. Another reason is that every group G = Omega G; Delta; e gives rise to a naturally correlated relation algebra CmG, called the complex, or Frobenius, algebra of G. See [JT48]; the observation that Frobenius algebras are relation algebras was first made by J. C. C. McKinsey. The complex algebra CmG is the Boolean algebra of all subsets of G together with the multiplication and inversion of complexes (subsets of G) and the singleton complex feg. CmG Sb(G) ....

....proof has two easily eliminated uses of associativity. See the remarks prior to Theorem 8. The next theorem is taken from [Ma78a] pp. 103 106, and [JT52] Theorem 4.10. The equivalence of (ff) and (fl) for relation algebras is due to McKinsey and Tarski, and is announced without proof in [JT48], result 4. The equivalence of (ff) fl) and (ffi) for relation algebras is also due to McKinsey and Tarski, and is stated without proof in [CT51] p. 362. The equivalence of (ff) fi) fl) and (ffi) is proved for relation algebras in Theorem 4.10 of [JT52] The part of that proof which shows ....

Bjarni J'onsson and Alfred Tarski, Representation problems for relation algebras, Abstract 89, Bulletin of the American Mathematical Society 54 (1948), 80 and 1192.

.... Boole [4] and Augustus De Morgan [35] 36] to create a calculus of relations that was extensively developed by Ernst Schroder [50] A fragment of this calculus was axiomatized by Alfred Tarski [52] Tarski s axiomatization, in a slightly altered form, became the definition of relation algebras [6] [25] [27] For further introductory and historical material on relation algebras see [6] 23] 24] 27] 32] 33] and [54] This section contains just enough basic definitions and results for the applications given later. Most of the material in this section can be found in [6] or [27] ....

Bjarni J'onsson and Alfred Tarski, Representation problems for relation algebras, Bulletin of the American Mathematical Society 54 (1948), 80 and 1192, Abstract 89.

....and Ernst Schroder ( S1895] Peirce introduced quantifiers into logic ( P1885] as a means of clarification and computation in the calculus of relations. Alfred Tarski continued Peirce s example 55 years later ( T41] and his work led to his definition of relation algebras in the late 1940 s ([JT48]) By that time first order logic was developed sufficiently for it to be used as a model for the construction of other algebras, such as cylindric algebras by Tarski, and polyadic algebras by Halmos. But the investigation of proper relation algebras was well under way prior to the introduction of ....

Bjarni J'onsson and Alfred Tarski, Representation problems for relation algebras, Abstract 89, Bulletin of the American Mathematical Society 54 (1948), 80 and 1192.

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Bjarni J'onsson and Alfred Tarski, Representation problems for relation algebras, Abstract 89, Bulletin of the American Mathematical Society 54 (1948), 80 and 1192.

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