Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2025
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| Accesso online: | https://doi.org/10.5281/zenodo.18110552 |
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Sommario:
- <div>Mathematical Applications of Science Fiction</div> <div> </div> <p>We establish a canonical correspondence between the con-<br>sistency strength of the Proper Forcing Axiom (PFA) and<br>the existence of Woodin cardinals within the core model<br>K. Specifically, we demonstrate that if PFA holds, then for<br>every set X, the inner model K(X) admits a proper class<br>of Woodin cardinals, or exhibits a failure of covering at a<br>measurable cardinal. We construct a fine-structural analysis<br>of the hierarchy of extender models L[⃗E] to show that the<br>failure of □κ principles, implied by PFA, necessitates the ex-<br>istence of δ-strong cardinals in the core model which reflect<br>to Woodin cardinals under generic absoluteness. This work<br>synthesizes the Core Model Induction with Steel’s analysis<br>of the PFA conjecture, providing a transfinite lower bound<br>for the consistency strength of proper forcing in terms of<br>inner model theory.</p>