论文信息 - Organic and tight

Organic and tight

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 (Theorem 3) and stationary many sets that are organic but not tight (Theorem 4). Working in the Constructible Universe, we give a characterization of organic and tight sets in terms of fine structure (Theorem 7). 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 (2006) 55–75] about the combinatorial principle Coherent Squares (Corollary 9).

James Cummings | Ernest Schimmerling | Matthew Foreman

[1] Lee J. Stanley,et al. Condensation-coherent global square systems , 1985 .

[2] Philip D. Welch,et al. On the Strength of Mutual Stationarity , 2006 .

[3] R. Jensen,et al. The fine structure of the constructible hierarchy , 1972 .

[4] Ralf Schindler,et al. MUTUAL STATIONARITY IN THE CORE MODEL , 2005 .

[5] Matthew Foreman,et al. Mutually stationary sequences of sets and the non-saturation of the non-stationary ideal onPϰ(λ) , 2001 .

[6] Matthew Foreman,et al. A very weak square principle , 1997, Journal of Symbolic Logic.

[7] James Cummings,et al. Canonical structure in the universe of set theory: part one , 2004, Ann. Pure Appl. Log..

[8] James Cummings,et al. The non-compactness of square , 2003, Journal of Symbolic Logic.

[9] James Cummings,et al. Squares, scales and stationary Reflection , 2001, J. Math. Log..

[10] James Cummings,et al. Canonical structure in the universe of set theory: part two , 2006, Ann. Pure Appl. Log..