{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86901"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86901","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach","abstract":"This thesis introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods and framework provided by the model theory of iterative differential fields. After defining what we mean by a strongly normal extension of iterative differential fields, we prove that these extensions have good Galois theory and that a G-primitive element theorem holds. Then, making use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations.","abstract_html":"This thesis introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods and framework provided by the model theory of iterative differential fields. After defining what we mean by a strongly normal extension of iterative differential fields, we prove that these extensions have good Galois theory and that a G-primitive element theorem holds. Then, making use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations.","abstract_has_math":false,"creators":["Moreno, Javier A."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Henson, C. 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