Global Reflection Principles

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic
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Maximality Principles in Set Theory.Luca Incurvati - forthcoming - Philosophia Mathematica:nkw011.
Richness and Reflection.Neil Barton - 2015 - Philosophia Mathematica 24 (3):330-359.

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