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Explicit Formulas for the Jump of Q-degrees


Crawshaw, Mark (1985) Explicit Formulas for the Jump of Q-degrees. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/b0x4-c027.


In the context of the axiom of projective determinacy, Q-degrees have been proposed as the appropriate generalisations of the hyperdegrees to all the odd levels of the projective hierarchy. In chapter one we briefly review the basics of Q-theory.

In the second chapter we characterise the Q-jump operation in terms of certain two-person games and derive an explicit formula for the Q-jump. This makes clear the similarities between the Q-degrees and the constructibility degrees, the Q-jump operation being a natural generalisation of the sharp operation.

In chapter three we mix our earlier results with some forcing techniques to get a new proof of the jump inversion theorem for Q-degrees. We also extend some results about minimal covers in hyperdegrees to the Q-degrees. Many of our methods are immediately applicable to the constructible degrees and provide new proofs of old results.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Becker, Howard Starr (chair)
  • Lorden, Gary A.
  • Luxemburg, W. A. J.
  • Wales, David B.
  • Kechris, Alexander S.
Defense Date:17 September 1984
Funding AgencyGrant Number
Record Number:CaltechTHESIS:01232017-115539334
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10020
Deposited By: Benjamin Perez
Deposited On:23 Jan 2017 21:45
Last Modified:27 Feb 2021 02:02

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