Sublogarithmic-transexponential series

2022/11/12 by Adele Padgett, Padgett, Adele
Mathematics · #03C64 (Primary) 03C60 #12H10 #16W60 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2211.06736

openalex publication_date 2022/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We adapt the construction of the field of logarithmic-exponential transseries of van den Dries, Macintyre, and Marker to build an ordered differential field of sublogarithmic-transexponential series. We use this structure to build a transexponential Hardy field closed under composition. Specifically, we prove that the germs at +∞ of L_transexp-terms in a single variable are ordered, where L_transexp is a language containing L_an(exp,log) with new symbols for a transexponential function, its derivatives, and their compositional inverses.

Related

• Ordered transexponential fields
• Constant power maps on Hardy fields and transseries
• Analytic continuations of log-exp-analytic germs
• Tame pairs of transseries fields
• Model completeness for the differential field of transseries with exponentiation