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 Title: Truncation in differential Hahn fields Author(s): Camacho Ahumada, Santiago Director of Research: van den Dries, Lou Doctoral Committee Chair(s): Hieronymi, Philipp Doctoral Committee Member(s): Tserunyan, Anush; Walsberg, Erik Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Valued Fields Transseries Truncation Differential Algebra Hahn Fields Abstract: Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation we show that generalized series fields with truncation as an extra primitive yields undecidability in several settings. Our main results, however, concern the robustness of being truncation closed in generalized series fields equipped with a derivation, and under extension procedures that involve this derivation. In the last chapter we study this in the ambient field T of logarithmic-exponential transseries. It leads there to a theorem saying that under a natural splitting'' condition the Liouville closure of a truncation closed differential subfield of T is again truncation closed. Issue Date: 2018-01-10 Type: Text URI: http://hdl.handle.net/2142/100890 Rights Information: Copyright 2018 Santiago Camacho Ahumada Date Available in IDEALS: 2018-09-04 Date Deposited: 2018-05