Reflective Cardinals
Dmytro Taranovsky
TL;DR
This paper introduces the concept of reflective cardinals, providing axioms and semantics for higher order set theory, and investigates their relationship with large cardinal axioms.
Contribution
It formalizes reflective cardinals, offering a new framework for understanding higher order set theory and its connection to large cardinal axioms.
Findings
Defined and axiomatized reflective cardinals
Provided semantics for higher order set theory
Explored links between reflective cardinals and large cardinals
Abstract
We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Rings, Modules, and Algebras