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A finite family weak square principle. (English) Zbl 0948.03043
The finite family weak square principle from the title is like \(\square_\kappa\), but with ‘one’ replaced by ‘finitely many’: \(\square_\kappa^{<\omega}\) means there is \(\langle\mathcal F_\gamma:\kappa<\gamma<\kappa^+, \gamma\) a limit\(\rangle\), where each \(\mathcal F_\gamma\) is a finite family of club subsets of \((\kappa,\gamma)\) such that if \(C\in\mathcal F_\gamma\) then \(\text{tp}C\leq\kappa\) and \(C\cap\delta\in\mathcal F_\delta\) whenever \(\delta\in\lim(C)\). The author proves that \(\square_\kappa^{<\omega}\) (for all \(\kappa\)) holds in certain core models.
Reviewer: K.P.Hart (Delft)

03E05 Other combinatorial set theory
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
Full Text: DOI
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