On Morley's Categoricity Theorem with an Eye Toward Forking

Released on by Colin N. Craft
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  • On Morley's Categoricity Theorem with an Eye Toward Forking Book Detail

  • Author : Colin N. Craft
  • Release Date : 2011
  • Publisher :
  • Genre : Model theory
  • Pages : 65
  • ISBN 13 :
  • File Size : 13,13 MB
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On Morley's Categoricity Theorem with an Eye Toward Forking by Colin N. Craft PDF Summary

Book Description: The primary result of this paper is Morley's Categoricity Theorem that a complete theory T which is k-catecorigal for some uncountable cardinal k is ^-categorical for every uncountable cardinal ^. We prove this by proving a characterization of uncountably categorical theories due to Baldwin and Lachlan. Before the actual statement and proof of Morley's theorem, we give an overview of the prerequisites from mathematical logic needed to understand the theorem and its proof. After proving Morley's theorem we briefly indicate some possible directions of further study having to do with forking and the related notion of independence of types.

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