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.
