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A strengthening of Jensen's □ principles

Aaron Beller & Ami Litman

Journal of Symbolic Logic 45 (2):251-264 (1980)

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In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.details James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied (...) Download Export citation Bookmark
Categoricity results for "L"[infinity]kappa>-free algebras.P. C. Eklof - 1988 - Annals of Pure and Applied Logic 37 (1):81.details Download Export citation Bookmark 2 citations
Categoricity results for< i> L_< sub>∞ κ.Paul C. Eklof & Alan H. Mekler - 1988 - Annals of Pure and Applied Logic 37 (1):81-99.details Download Export citation Bookmark 1 citation
The primal framework II: smoothness.J. T. Baldwin & S. Shelah - 1991 - Annals of Pure and Applied Logic 55 (1):1-34.details Let be a class of models with a notion of ‘strong’ submodel and of canonically prime model over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth , then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with homogeneous-universal. Download Export citation Bookmark 7 citations
On the size of closed unbounded sets.James E. Baumgartner - 1991 - Annals of Pure and Applied Logic 54 (3):195-227.details We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under a large (...) Download Export citation Bookmark 18 citations
Categoricity results for L∞κ.Paul C. Eklof & Alan H. Mekler - 1988 - Annals of Pure and Applied Logic 37 (1):81-99.details Download Export citation Bookmark 4 citations
Abstract classes with few models have `homogeneous-universal' models.J. Baldwin & S. Shelah - 1995 - Journal of Symbolic Logic 60 (1):246-265.details Download Export citation Bookmark 3 citations
Square below a non-weakly compact cardinal.Hazel Brickhill - 2020 - Archive for Mathematical Logic 59 (3-4):409-426.details In his seminal paper introducing the fine structure of L, Jensen proved that under \ any regular cardinal that reflects stationary sets is weakly compact. In this paper we give a new proof of Jensen’s result that is straight-forward and accessible to those without a knowledge of Jensen’s fine structure theory. The proof here instead uses hyperfine structure, a very natural and simpler alternative to fine structure theory introduced by Friedman and Koepke. Download Export citation Bookmark
Generalisations of stationarity, closed and unboundedness, and of Jensen's □.H. Brickhill & P. D. Welch - 2023 - Annals of Pure and Applied Logic 174 (7):103272.details Download Export citation Bookmark 1 citation

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