Smooth categories and global □

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Annals of Pure and Applied Logic 102 (1-2):101-138 (2000)
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Abstract

We shall construct a smooth category of mice and embeddings in the core model for measures of order 0. The existence of such a category implies that the global principle □ holds in K. We then prove a much stronger, the so-called condensation-coherent version of global □. The key tool of the whole construction is a new criterion on preserving soundness under condensation

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10.1016/s0168-0072(99)00020-2

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Citations of this work

Square in core models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
Global square sequences in extender models.Martin Zeman - 2010 - Annals of Pure and Applied Logic 161 (7):956-985.
◇ at Mahlo cardinals.Martin Zeman - 2000 - Journal of Symbolic Logic 65 (4):1813-1822.
Square In Core Models, By, Pages 305 -- 314.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
Global square and mutual stationarity at the ℵn.Peter Koepke & Philip D. Welch - 2011 - Annals of Pure and Applied Logic 162 (10):787-806.

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References found in this work

The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Combinatorial principles in the core model for one Woodin cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
The covering lemma for K.Tony Dodd & Ronald Jensen - 1982 - Annals of Mathematical Logic 22 (1):1-30.
The covering lemma for L[U].A. J. Dodd & R. B. Jensen - 1982 - Annals of Mathematical Logic 22 (2):127-135.

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