Abstract
H-fields are ordered differential fields that capture some basic properties of Hardy fields and fields of transseries. Each H-field is equipped with a convex valuation, and solving first-order linear differential equations in H-field extensions is strongly affected by the presence of a "gap" in the value group. We construct a real closed H-field that solves every first-order linear differential equation, and that has a differentially algebraic H-field extension with a gap. This answers a question raised in [1]. The key is a combinatorial fact about the support of transseries obtained from iterated logarithms by algebraic operations, integration, and exponentiation.
Original language | English (US) |
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Pages (from-to) | 247-280 |
Number of pages | 34 |
Journal | Selecta Mathematica, New Series |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2005 |
Keywords
- Fields of transseries
- H-fields
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy