On Morley's Categoricity Theorem with an Eye Toward Forking

Download or read book On Morley's Categoricity Theorem with an Eye Toward Forking written by Colin N. Craft and published by . This book was released on 2011 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.