(Weak) diamond can fail at the least inaccessible cardinal
Mohammad Golshani
TL;DR
This paper demonstrates how to force the failure of the weak diamond principle at the least inaccessible cardinal starting from large cardinal assumptions, improving previous results by Woodin and others.
Contribution
It introduces a method to force the failure of weak diamond at the least inaccessible cardinal, advancing understanding of combinatorial principles at large cardinals.
Findings
Weak diamond can be made to fail at the least inaccessible cardinal.
The method improves upon previous unpublished and published results.
The approach relies on large cardinal assumptions and forcing techniques.
Abstract
Starting from suitable large cardinals, we force the failure of (weak) diamond at the least inaccessible cardinal. The result improves an unpublished theorem of Woodin and a recent result of Ben-Neria, Garti and Hayut.
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