Contents of Measure Theory, by D.H.Fremlin

Introduction to Volume 5

Chapter 51: Cardinal functions

511 Definitions
Cardinal functions of partially ordered sets, topological spaces and Boolean algebras; precalibers; ideals of sets.

512 Galois-Tukey connections
Supported relations; Galois-Tukey connections; covering numbers, additivity, saturation, linking numbers; simple products; sequential composition of supported relations.

513 Partially ordered sets
Saturation and the Erdös-Tarski theorem; cofinalities of cardinal functions; Tukey functions; Tukey equivalence; σ-additivities; *metrizably compactly based directed sets; *measurable Tukey functions.

514 Boolean algebras
Stone spaces; cardinal functions of Boolean algebras; order-preserving functions of Boolean algebras; regular open algebras; regular open algebras of partially ordered sets; finite-support products.

515 The Balcar-Franek theorem
Boolean-independent sets; free subalgebras; refining systems; the Balcar-Franek theorem; the Pierce-Koppelberg theorem.

516 Precalibers
Precalibers of supported relations; and Galois-Tukey connections; partially ordered sets, topological spaces and Boolean algebras; saturation and linking numbers; saturation of product spaces.

517 Martin numbers
Characterizations of m(P); regular open algebras, Stone spaces and Novak numbers; precalibers, saturation and weak distributivity; mcountable and p.

518 Freese-Nation numbers
Freese-Nation numbers of partially ordered sets; Boolean algebras; upper and lower bounds for FN(A) under special axioms; tight filtrations and Geschke systems; large algebras are not tightly filtered.

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Revised 2.10.08