The Diagonal Strong Reflection Principle and its Fragments

Journal of Symbolic Logic 88 (3):1281-1309 (2023)
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Abstract

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.

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References found in this work

Diagonal reflections on squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.
Separating stationary reflection principles.Paul Larson - 2000 - Journal of Symbolic Logic 65 (1):247-258.
Canonical fragments of the strong reflection principle.Gunter Fuchs - 2021 - Journal of Mathematical Logic 21 (3):2150023.

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