×

zbMATH — the first resource for mathematics

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:
03E05 Other combinatorial set theory
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/0003-4843(72)90001-0 · Zbl 0257.02035
[2] The core model iterability problem 8 (1996) · Zbl 0864.03035
[3] DOI: 10.1016/0168-0072(93)90037-E · Zbl 0805.03043
[4] Fine structure for tame inner models 61 pp 621– (1996)
[5] Set theory: techniques and applications
[6] DOI: 10.4310/MRL.1995.v2.n5.a6 · Zbl 0847.03024
[7] A weak Dodd-Jensen lemma 64 pp 1285– (1999)
[8] DOI: 10.1016/0168-0072(94)00036-3 · Zbl 0834.03018
[9] Fine structure and iteration trees (1994) · Zbl 0805.03042
[10] DOI: 10.1016/S0168-0072(96)00032-2 · Zbl 0868.03021
[11] Transactions of the American Mathematical Society
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.