Diagonal reflections on squares

Archive for Mathematical Logic 58 (1-2):1-26 (2019)
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Abstract

The effects of the forcing axioms \, \ and \ on the failure of weak threaded square principles of the form \\) are analyzed. To this end, a diagonal reflection principle, \, and it implies the failure of \\) if \. It is also shown that this result is sharp. It is noted that \/\ imply the failure of \\), for every regular \, and that this result is sharp as well.

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Citations of this work

Aronszajn Tree Preservation and Bounded Forcing Axioms.Gunter Fuchs - 2021 - Journal of Symbolic Logic 86 (1):293-315.

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References found in this work

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
Set Mapping Reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
Resurrection Axioms and Uplifting Cardinals.Joel David Hamkins & Thomas A. Johnstone - 2014 - Archive for Mathematical Logic 53 (3-4):463-485.

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