We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
123 \(\Rightarrow\) 62 |
Two model theoretic ideas in independence proofs, Pincus, D. 1976, Fund. Math. |
62 \(\Rightarrow\) 308-p |
Maximal p-subgroups and the axiom of choice, Howard-Yorke-1987 [1987, Notre Dame J. Formal Logic |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
123: | \(SPI^*\): Uniform weak ultrafilter principle: For each family \(F\) of infinite sets \(\exists f\) such that \(\forall x\in F\), \(f(x)\) is a non-principal ultrafilter on \(x\). |
62: | \(C(\infty,< \aleph_{0})\): Every set of non-empty finite sets has a choice function. |
308-p: | If \(p\) is a prime and if \(\{G_y: y\in Y\}\) is a set of finite groups, then the weak direct product \(\prod_{y\in Y}G_y\) has a maximal \(p\)-subgroup. |
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