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Diagonal reflections on squares

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

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The Diagonal Strong Reflection Principle and its Fragments.C. O. X. Sean D. & Gunter Fuchs - 2023 - Journal of Symbolic Logic 88 (3):1281-1309.details A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms. Download Export citation Bookmark 1 citation
Separating diagonal stationary reflection principles.Gunter Fuchs & Chris Lambie-Hanson - 2021 - Journal of Symbolic Logic 86 (1):262-292.details We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences. Download Export citation Bookmark 3 citations
Errata: on the role of the continuum hypothesis in forcing principles for subcomplete forcing.Gunter Fuchs - forthcoming - Archive for Mathematical Logic:1-13.details In this note, I will list instances where in the literature on subcomplete forcing and its forcing principles (mostly in articles of my own), the assumption of the continuum hypothesis, or that we are working above the continuum, was omitted. I state the correct statements and provide or point to correct proofs. There are also some new results, most of which revolve around showing the necessity of the extra assumption. Download Export citation Bookmark
Aronszajn tree preservation and bounded forcing axioms.Gunter Fuchs - 2021 - Journal of Symbolic Logic 86 (1):293-315.details I investigate the relationships between three hierarchies of reflection principles for a forcing class $\Gamma $ : the hierarchy of bounded forcing axioms, of $\Sigma ^1_1$ -absoluteness, and of Aronszajn tree preservation principles. The latter principle at level $\kappa $ says that whenever T is a tree of height $\omega _1$ and width $\kappa $ that does not have a branch of order type $\omega _1$, and whenever ${\mathord {\mathbb P}}$ is a forcing notion in $\Gamma $, then it is (...) Download Export citation Bookmark 1 citation

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