Equiconsistencies at subcompact cardinals

  title={Equiconsistencies at subcompact cardinals},
  author={Itay Neeman and John R. Steel},
  journal={Archive for Mathematical Logic},
  • I. NeemanJ. Steel
  • Published 1 February 2016
  • Mathematics
  • Archive for Mathematical Logic
We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □(δ) and □δ fail, then δ is subcompact in a class inner model. If in addition □(δ+) fails, we prove that δ is $${\Pi_1^2}$$Π12 subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. As a corollary we also see that assuming the existence of a Woodin cardinal δ so that SBH… 

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