Material set theory

Countable Principle of Choice

The Countable Axiom of Choice is a possible axiom of material set theory and rather weak choice principle:¹ set

which is to say, if is a set and is a left-total Relation set, i.e. relates every with at least one , then there exists a choice function that selects such a for each . Thus countable sequences of independent choices are always possible.

Relationship to other axioms

Strengthenings

Over ZF, is a strict weakening of the Axiom of Dependent Choice and thus the Axiom of Choice.

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Footnotes

1. 2006. Notes on set theory, ¶8.12, p. 114 ↩