
TL;DR
This paper provides an introductory overview of the hierarchy of large cardinals in set theory, explaining their significance, definitions, and connections to foundational questions like the Continuum Hypothesis.
Contribution
It offers a clear, accessible survey of large cardinal concepts, their motivations, and their role in understanding the higher infinite in set theory.
Findings
Clarifies the hierarchy of large cardinals
Explores connections with the Continuum Hypothesis
Provides philosophical reflections on consistency beliefs
Abstract
The purpose of this paper is to provide an introductory overview of the large cardinal hierarchy in set theory. By a large cardinal, we mean any cardinal whose existence is strong enough of an assumption to prove the consistency of ZFC. We assume basic familiarity with set theory, model theory, and the ZFC axioms, though certain concepts will be reviewed as necessary. We attempt to clarify the vast landscape of the higher infinite, motivating the definitions of some (but certainly not all) of the known large cardinals. We also discuss connections with the Continuum Hypothesis and provide some philosophical reflections on belief in the consistency of large cardinals.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Philosophy and History of Science
