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The Ramsey property and degrees in the analytical hierarchy

Citation

Kastanas, Ilias George (1981) The Ramsey property and degrees in the analytical hierarchy. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:01202017-152612696

Abstract

In Chapter I we review some known results about the Ramsey theory for partitions of reals, and we present a certain two-person game such that if either player has a winning strategy then a homogeneous set for the partition can be constructed, and conversely. This gives alternative proofs of some of the known results. We then discuss possible uses of the game in obtaining effective versions and prove a theorem along these lines.

In Chapter II we study the structure of initial segments of the Δ12n+1-degrees, assuming Projective Determinacy. We show that every finite distributive lattice is isomorphic to such an initial segment, and hence that the first-order theory of the ordering of Δ12n+1-degrees is undecidable.

In Chapter III we extend Friedberg's Jump Inversion theorem to Q2n+1-degrees, after noticing that it fails tor Δ12n+1-degrees. We assume again Projective Determinacy.

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:Restricted to Caltech community only
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Unknown, Unknown
Defense Date:26 January 1981
Record Number:CaltechTHESIS:01202017-152612696
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:01202017-152612696
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10018
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:23 Jan 2017 16:15
Last Modified:23 Jan 2017 16:15

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