Description:
Equivalences in Feferman's model, \(\cal M2\) shown in Truss [1978]
Content:
Truss [1978] shows that in Feferman's model, \(\cal M2\) (Feferman [1965]), the following hold:
- \(\forall \) ordinals \(\alpha\), \(2^{\aleph_{\alpha}} =\aleph_{\alpha +1}\cdot 2^{\aleph_{0}}\)
- For all \(X\), if \([X]^{2}\) has a choice function, then \(\exists\alpha\) such that \(|X| \le 2^{\aleph_{\alpha}}\).
- Form 40 (\(C(WO,\infty )\)).
- \({\cal P}(\omega)\) has no non-principal prime ideal, (the negation of Form 70).
- \(\neg C(\infty,2)\), (the negation of Form 88).
- There is a partition of \({\cal P}(\omega)\) into non-empty subsets without a choice function, (the negation of Form 203).
- Form 204, For every infinite \(X\) there is a function from\(X\) onto \(2 \times X\).
Howard-Rubin number:
65
Type:
Results
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