Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Krapp, Lothar Sebastian"'
We give an explicit algebraic characterisation of all definable henselian valuations on a dp-minimal real field. Additionally we characterise all dp-minimal real fields that admit a definable henselian valuation with real closed residue field. We do
Externí odkaz:
http://arxiv.org/abs/2410.10344
Autor:
Krapp, Lothar Sebastian, Wirth, Laura
The Fundamental Theorem of Statistical Learning states that a hypothesis space is PAC learnable if and only if its VC dimension is finite. For the agnostic model of PAC learning, the literature so far presents proofs of this theorem that often tacitl
Externí odkaz:
http://arxiv.org/abs/2410.10243
Autor:
Bagayoko, Vincent, Krapp, Lothar Sebastian, Kuhlmann, Salma, Panazzolo, Daniel, Serra, Michele
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our knowledge
Externí odkaz:
http://arxiv.org/abs/2403.05827
We develop a first-order theory of ordered transexponential fields in the language $\{+,\cdot,0,1,<,e,T\}$, where $e$ and $T$ stand for unary function symbols. While the archimedean models of this theory are readily described, the study of the non-ar
Externí odkaz:
http://arxiv.org/abs/2305.04607
Autor:
Krapp, Lothar Sebastian
Publikováno v:
Bull. Lond. Math. Soc. 56 (2024) 907-913
Motivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o-minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embed
Externí odkaz:
http://arxiv.org/abs/2302.01609
Publikováno v:
Model Th. 2 (2023) 101-120
We study the definability of convex valuations on ordered fields, with a particular focus on the distinguished subclass of henselian valuations. In the setting of ordered fields, one can consider definability both in the language of rings $\mathcal{L
Externí odkaz:
http://arxiv.org/abs/2206.15301
In 1882, Kronecker established that a given univariate formal Laurent series over a field can be expressed as a fraction of two univariate polynomials if and only if the coefficients of the series satisfy a linear recurrence relation. We introduce th
Externí odkaz:
http://arxiv.org/abs/2206.04126
Publikováno v:
J. Symb. Log. 2022
Given a henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any henselian valuation whose value group is not closed in its divisible hull is definable in the language o
Externí odkaz:
http://arxiv.org/abs/2105.09234
Publikováno v:
MLQ Math. Log. Q. 67 (2021) 321-328
The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or admits a non-trivial definable henselian valuation, in the language of rings. We specialise this conjecture to ordered f
Externí odkaz:
http://arxiv.org/abs/2010.14770
Publikováno v:
Forum Mathematicum, vol. 33, no. 4, 2021, pp. 953-972
In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the language of o
Externí odkaz:
http://arxiv.org/abs/2010.11832