We have the following indirect implication of form equivalence classes:
Implication | Reference |
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379 \(\Rightarrow\) 73 |
Weak choice principles, De la Cruz, O. 1998a, Proc. Amer. Math. Soc. Set Theory: Techniques and Applications, De la Cruz/Di Prisco, 1998b, 47-70 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
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379: | \(PKW(\infty,\infty,\infty)\): For every infinite family \(X\) of sets each of which has at least two elements, there is an infinite subfamily \(Y\) of \(X\) and a function \(f\) such that for all \(y\in Y\), \(f(y)\) is a non-empty proper subset of \(y\). |
73: | \(\forall n\in\omega\), \(PC(\infty,n,\infty)\): For every \(n\in\omega\), if \(C\) is an infinite family of \(n\) element sets, then \(C\) has an infinite subfamily with a choice function. De la Cruz/Di Prisco [1998b] |
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