TL;DR
This paper develops the fine structure theory of the minimal model under the Largest Suslin Axiom, proving key conjectures and implications related to set-theoretic axioms and models.
Contribution
It establishes the fine structure of the minimal model of the Largest Suslin Axiom and proves the Mouse Set Conjecture within this context.
Findings
The minimal model satisfies the Mouse Set Conjecture.
Proper Forcing Axiom implies the existence of the minimal model.
Advances the understanding of models satisfying the Largest Suslin Axiom.
Abstract
We develop the basic fine structure theory of the minimal model of the Largest Suslin Axiom. In particular, we prove that that the minimal model of the Largest Suslin Axiom satisfies the Mouse Set Conjecture, and that the Proper Forcing Axiom implies the minimal model of the Largest Suslin Axiom exists.
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