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# Algebras of Sets and Combinatorics

### About this Title

**L. Š. Grinblat**, *College of Judea and Samaria, Ariel, Israel*. Translated by **Alexander Stoyanovsky**

Publication: Translations of Mathematical Monographs

Publication Year:
2002; Volume 214

ISBNs: 978-0-8218-2765-9 (print); 978-1-4704-4639-0 (online)

DOI: https://doi.org/10.1090/mmono/214

MathSciNet review: MR1923171

MSC: Primary 03E05; Secondary 03E35, 28A05

### Table of Contents

**Front/Back Matter**

**Chapters**

- 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
- On a question of Grinblat