CMU Core Model Seminar (Spring 2026)

Meetings: Wednesdays 4:20-6pm in Wean 8220

Description

For 40 years or more, the large cardinal consistency strength of various failures of Jensen's square principles had been conjectured to be in the neighborhood of a supercompact cardinal. Recently, Blue, Larson and Sargsyan made the surprising discovery that the consistency strength of these principles had been vastly overestimated. Their new upper bounds are somewhat less than the existence of a Woodin cardinal that is a limit of Woodin cardinals. There are many components to their proofs, including large cardinals, inner models, derived models of determinacy, the HOD analysis and \(\mathbb{P}_{\mathrm{max}}\) forcing. The various components will be introduced and their essence discussed before they are used in the proofs of the main theorems.

Meeting 1 (January 21)

• Introduction & roadmap

References

1. Blue, Larson, Sargsyan, Nairian models.
2. Blue, Larson, Sargsyan, Failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals.
3. Larson, Extensions of the Axiom of Determinacy.
4. Larson, Forcing over models of determinacy. In Handbook of Set Theory.
5. Steel, A comparison process for mouse pairs.
6. Steel, Mouse pairs and Suslin cardinals.