Resplendent models generated by indiscernibles
Item
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Title
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Resplendent models generated by indiscernibles
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Identifier
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d_2009_2013:a97ef036c60b:11658
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identifier
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12216
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Creator
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Lee, Whanki,
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Contributor
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Roman Kossak
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Date
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2013
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Logic | Cofinal extension | Indiscernibles | Peano Arithmetic | Ramsey's Theorem | Recursive saturation | Resplendence
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Abstract
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As first proved by Ehrenfeucht and Mostowski [EM], every first-order theory which has infinite models, has models with infinite sets of indiscernibles. Ramsey's Theorem is a crucial component of the proof of this result. If the structure has built-in Skolem functions, taking the Skolem hull of the set of indiscernibles will produce structures generated by a set of indiscernibles.;In this thesis I study the question: Which first-order structures are generated by indiscernibles? J. Schmerl showed that if L is a finite language, every countable recursively saturated L -structure in which a form of coding of finite functions is available is generated by indiscernibles. Further, he showed that such a structure has arbitrarily large extensions which are generated by a set of indiscernibles, resplendent, and Linfinity,w -equivalent to the original structure. Proofs of these theorems are complex and use a combinatorial lemma whose proof in Schmerl's paper has an acknowledged gap. I offer a complete proof of a more direct combinatorial lemma from which Schmerl's theorems follow.;The other subject of this thesis is cofinal extensions of linearly ordered structures. It is related to the work of R. Kaye who used a weak notion of saturation to give a sufficient condition under which a countable model of PA- has a proper elementary cofinal extension. I give two different proofs of the fact that every countable recursively saturated linearly ordered structure with no last element has a proper cofinal elementary extension.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Mathematics
