HomePublications

Critical Cardinals

Research output: Contribution to journalArticle

Open Access permissions

Open

Documents

Links

DOI

Authors

Organisational units

Abstract

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings to symmetric extensions, and we use this to show that it is consistent relative to a supercompact cardinal that there is a critical cardinal whose successor is singular.

Details

Original languageEnglish
Pages (from-to)449–472
Number of pages24
JournalIsrael Journal of Mathematics
Volume236
Issue number1
Early online date4 Apr 2020
DOIs
Publication statusPublished - Apr 2020
Peer-reviewedYes

View graph of relations

ID: 157781475

Related by author
  1. Kelley-Morse set theory does not prove the class Fodor principle

    Research output: Contribution to journalArticle

  2. How to have more things by forgetting how to count them

    Research output: Contribution to journalArticle

  3. Dependent choice, properness, and generic absoluteness

    Research output: Contribution to journalArticle

  4. The Morris model

    Research output: Contribution to journalArticle

  5. Realizing Realizability Results with Classical Constructions

    Research output: Contribution to journalArticle

Related by journal
  1. Existentially closed exponential fields

    Research output: Contribution to journalArticle

  2. A generalization of Martin's Axiom

    Research output: Contribution to journalArticle

  3. On maximal subgroups of free idempotent generated semigroups

    Research output: Contribution to journalArticle

  4. A partition theorem for a large dense linear order

    Research output: Contribution to journalArticle