We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
311 \(\Rightarrow\) 142 | The Banach-Tarski Paradox, Wagon, [1985] |
142 \(\Rightarrow\) 280 | clear |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
311: | Abelian groups are amenable. (\(G\) is amenable if there is a finitely additive measure \(\mu\) on \(\cal P(G)\) such that \(\mu(G)=1\) and \(\forall A\subseteq G, \forall g\in G\), \(\mu(gA)=\mu(A)\).) |
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. |
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