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; **m**_{countable} 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