Binary Relations and Permutation Groups
Copyright policy )Binary Relations and Permutation Groups
AbstractWe discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surprising result that on such sets, logic with three variables is as powerful in expression as full first order logic.
- University of Ulster United Kingdom
- Hungarian Academy of Sciences Hungary
first order logic, Permutation groups, clones of operations, Cylindric and polyadic algebras; relation algebras, Operations and polynomials in algebraic structures, primal algebras, Galois closure, permutation groups, Classical first-order logic, Galois correspondences, closure operators (in relation to ordered sets), Galois connection, set relation algebras
first order logic, Permutation groups, clones of operations, Cylindric and polyadic algebras; relation algebras, Operations and polynomials in algebraic structures, primal algebras, Galois closure, permutation groups, Classical first-order logic, Galois correspondences, closure operators (in relation to ordered sets), Galois connection, set relation algebras
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