Axiom Of Choice

We have the following indirect implication of form equivalence classes:

88 \(\Rightarrow\) 280 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
88 \(\Rightarrow\) 142	The Axiom of Choice, Jech, 1973b, page 7 problem 11
142 \(\Rightarrow\) 280	clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
88:	\(C(\infty ,2)\): Every family of pairs has a choice function.
142:	\(\neg PB\): There is a set of reals without the property of Baire. Jech [1973b], p. 7.
280:	There is a complete separable metric space with a subset which does not have the Baire property.

Comment:

Back