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  1. A finite family weak square principle.Ernest Schimmerling - 1999 - Journal of Symbolic Logic 64 (3):1087-1110.
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  • A weak Dodd-Jensen lemma.Itay Neeman & John Steel - 1999 - Journal of Symbolic Logic 64 (3):1285-1294.
    We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.
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  • A Weak Dodd-jensen Lemma.Itay Neeman & John Steel - 1999 - Journal of Symbolic Logic 64 (3):1285-1294.
    We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.
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  • Square In Core Models, By, Pages 305 -- 314.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
    We prove that in all Mitchell-Steel core models, □k holds for all k. From this we obtain new consistency strength lower bounds for the failure of □k if k is either singular and countably closed, weakly compact, or measurable. Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □k holds iff k is not subcompact.
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  • Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
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  • The Jensen covering property.E. Schimmerling & W. H. Woodin - 2001 - Journal of Symbolic Logic 66 (4):1505-1523.
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  • Square in core models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
    We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ κ holds (...)
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  • Deconstructing inner model theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
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  • Combinatorial principles in the core model for one Woodin cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
    We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, λ □κ, (...)
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  • Inner models in the region of a Woodin limit of Woodin cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
    We extend the construction of Mitchell and Steel to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.
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  • The covering lemma up to a Woodin cardinal.W. J. Mitchell, E. Schimmerling & J. R. Steel - 1997 - Annals of Pure and Applied Logic 84 (2):219-255.
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  • The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
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  • Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
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  • Constructibility.Keith J. Devlin - 1987 - Journal of Symbolic Logic 52 (3):864-867.
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  • Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
    Since the work of Gödel and Cohen, which showed that Hilbert's First Problem was independent of the usual assumptions of mathematics, there have been a myriad of independence results in many areas of mathematics. These results have led to the systematic study of several combinatorial principles that have proven effective at settling many of the important independent statements. Among the most prominent of these are the principles diamond and square discovered by Jensen. Simultaneously, attempts have been made to find suitable (...)
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  • The weak □* is really weaker than the full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
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  • [Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
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  • The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
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