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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)

##### MSC:
 300000 Other combinatorial set theory 3e+45 Inner models, including constructibility, ordinal definability, and core models 3e+55 Large cardinals
##### Keywords:
square principle; core model
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##### References:
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