Director of Research (if dissertation) or Advisor (if thesis)
van den Dries, Lou
Doctoral Committee Chair(s)
Hieronymi, Philipp
Committee Member(s)
Tserunyan, Anush
Walsberg, Erik
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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