Organic and tight

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Annals of Pure and Applied Logic 160 (1):22-32 (2009)
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Abstract

We define organic sets and organically stationary sequences, which generalize tight sets and tightly stationary sequences respectively. We show that there are stationary many inorganic sets and stationary many sets that are organic but not tight. Working in the Constructible Universe, we give a characterization of organic and tight sets in terms of fine structure. We answer a related question posed in [J. Cummings, M. Foreman, M. Magidor, Canonical structure in the universe of set theory: Part two, Ann. Pure Appl. Logic 142 55–75] about the combinatorial principle Coherent Squares.

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10.1016/j.apal.2009.01.016

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Citations of this work

Tight stationarity and tree-like scales.William Chen - 2015 - Annals of Pure and Applied Logic 166 (10):1019-1036.
Full reflection at a measurable cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
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 fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
A very weak square principle.Matthew Foreman & Menachem Magidor - 1997 - Journal of Symbolic Logic 62 (1):175-196.
Condensation-coherent global square systems.Hans-Dieter Donder, Ronald B. Jensen & Lee J. Stanley - 1985 - In Anil Nerode & Richard A. Shore (eds.), Recursion Theory. American Mathematical Society. pp. 42--237.

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