The notion of a BooLEan algebra with operators was introduced by J~NSSON and TARSKI [ 5 ] . It encompasses as special cases relation algebras (TARSKI [9]), closure algebras (MCKINSEY-TARSKI [S]), cylindric algebras (HENRIN-TARSKI [4]), polyadic algebras (HALMOS [Z]), and other algebras which have be
On Boolean Algebras and their Recursive Completions
β Scribed by E. W. Madison
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 310 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0044-3050
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π SIMILAR VOLUMES
Lct 1 be an infinite cardinal and let A , B be Boolean algebras. A homomorphism h: , 4 4 B is said to be A-cmpkte if whenever X is a subset of A of cardinality I such that the join V X of X exists in A , then V h[X] exists in B and is equal to h(V X ) . If x is an infinite cardinal, B is said to be
I ) The second author's contribution to the paper comes out of his Ph. D. dissertation written 21' under the supervision of Prof. TAKEUTI to whom the author is grateful. Math. (2) 94 (1971), 201 -245.
Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2 d sets forming a d-dimensional Boolean algebra. We review extremal results for each of these classes and derive new ones for Bool