Adding Closed Unbounded Subsets of ω₂ with Finite Forcing

Notre Dame Journal of Formal Logic 46 (3):357-371 (2005)
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Abstract

An outline is given of the proof that the consistency of a κ⁺-Mahlo cardinal implies that of the statement that I[ω₂] does not include any stationary subsets of Cof(ω₁). An additional discussion of the techniques of this proof includes their use to obtain a model with no ω₂-Aronszajn tree and to add an ω₂-Souslin tree with finite conditions

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10.1305/ndjfl/1125409334

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William Mitchell
University of Alabama, Birmingham

Citations of this work

Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Forcing with adequate sets of models as side conditions.John Krueger - 2017 - Mathematical Logic Quarterly 63 (1-2):124-149.
Fragility and indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
Two applications of finite side conditions at omega _2.Itay Neeman - 2017 - Archive for Mathematical Logic 56 (7-8):983-1036.

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References found in this work

Reflecting stationary sets and successors of singular cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Adding a closed unbounded set.J. E. Baumgartner, L. A. Harrington & E. M. Kleinberg - 1976 - Journal of Symbolic Logic 41 (2):481-482.
A weak variation of Shelah's I[ω₂].William J. Mitchell - 2004 - Journal of Symbolic Logic 69 (1):94-100.

View all 9 references / Add more references