Algebras of Sets and Combinatorics 0821827650, 9780821827659
An algebra $A$ on a set $X$ is a family of subsets of this set closed under the operations of union and difference of tw
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English, Russian Pages 256 [264] Year 2002
Table of contents :
Content: Introduction Main results The main idea Finite sequences of algebras (1). Proof of Theorems 2.1 and 2.2 Countable sequences of algebras (1). Proof of Theorem 2.4 Proof of the Gitik-Shelah theorem, and more from set theory Proof of Theorems 1.17, 2.7, 2.8 Theorems on almost $\sigma$-algebras. Proof of Theorem 2.9 Finite sequences of algebras (2). The function $\mathfrak{g}(n)$ A description of the class of functions $\Psi_*^7$ The general problem. Proof of Theorems 2.15 and 2.20 Proof of Theorems 2.21(1,3), 2.24 The inverse problem Finite sequences of algebras (3). Proof of Theorems 2.27, 2.31, 2.36, 2.38 Preliminary notions and lemmas Finite sequences of algebras (4). Proof of Theorems 2.39(1,2), 2.45(1,2) Countable sequences of algebras (2). Proof of Theorems 2.29, 2.32, 2.46 A refinement of theorems on $\sigma$-algebras. Proof of Theorems 2.34, 2.44 Semistructures and structures of sets. Proof of Theorem 2.48 Final comments. Generalization of Theorem 2.1 Appendix: On a question of Grinblat by S. Shelah Bibliography Index.
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