Abstract: The concept of cylindric algebras (CA) is created to permit the use of algebraic methods in treating two related parts of mathematics. One of these is a very general kind of geometry associated with basic set-theoretic notions, and the other is the theory of deductive systems of mathematical logic. The two domains are connected because models of deductive systems give rise in a natural way to structures within the set-theoretical “spaces”. The notion of a cylindric algebra can be considered as a common, algebraic abstraction from its two sources–.the set-theoretical source and the logical source and its relation. A cylindric set algebra is a collection of subsets of αU closed under all the Boolean and cylindric operations, having all diagonal hyperplanes as members. The abstract notion of a cylindric algebra is defined by equational axioms, which hold in all cylindric set algebras.
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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