3 citations · 15 across the 21 of their papers we have counts for
21 papers
Contributions to the hierarchy of probabilistic languages
Lothar Sebastian Krapp, Remo Nitschke
We reconsider the theory of probabilistic formal languages generated by n-gram models and by probabilistic context-free grammars (PCFGs). The expected hierarchy of probabilistic gr…
Ordered henselian valued fields: definability and Borel sets
Lothar Sebastian Krapp, Floris Vermeulen
We firstly show that due to their resplendency ordered henselian valued fields admit relative field quantifier elimination in the Denef--Pas language expanded by linear orders in t…
Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning
David Kattermann, Lothar Sebastian Krapp
We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental The…
Time-series Random Process Complexity Ranking Using a Bound on Conditional Differential Entropy
Jacob Ayers, Richard Hahnloser, Julia Ulrich +5
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. H…
Decomposing the automorphism group of the surreal numbers
Elliot Kaplan, Lothar Sebastian Krapp, Michele Serra
We study the automorphism group of the field of surreal numbers. Our main structure theorem presents a decomposition of this group into a product of five significant factors. Using…
On Tameness, Measurability and the Independence Property
Lothar Sebastian Krapp, Matthieu Vermeil, Laura Wirth
In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield of the real numbers th…
Definable ranks
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an order…
Definable henselian valuations on dp-minimal real fields
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
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…
Measurability in the Fundamental Theorem of Statistical Learning
Lothar Sebastian Krapp, Laura Wirth
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, t…
Automorphisms and derivations on algebras endowed with formal infinite sums
Vincent Bagayoko, Lothar Sebastian Krapp, Salma Kuhlmann +2
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 fi…
Ordered transexponential fields
Lothar Sebastian Krapp, Salma Kuhlmann
We develop a first-order theory of ordered transexponential fields in the language , where and stand for unary function symbols. While the archimedea…
Embedding the prime model of real exponentiation into o-minimal exponential fields
Lothar Sebastian Krapp
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…
Definable valuations on ordered fields
Philip Dittmann, Franziska Jahnke, Lothar Sebastian Krapp +1
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, o…
Generalised power series determined by linear recurrence relations
Lothar Sebastian Krapp, Salma Kuhlmann, Michele Serra
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 coefficien…
Definability of henselian valuations by conditions on the value group
Lothar Sebastian Krapp, Salma Kuhlmann, Moritz Link
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 gr…
Ordered fields dense in their real closure and definable convex valuations
Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy
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…
Strongly NIP almost real closed fields
Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy
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…
On Rayner structures
Lothar Sebastian Krapp, Salma Kuhlmann, Michele Serra
In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We characterise the set-theoretic and…
On Strongly NIP Ordered Fields and Definable Convex Valuations
Lothar Sebastian Krapp, Salma Kuhlmann, Gabriel Lehéricy
We investigate what henselian valuations on ordered fields are definable in the language of ordered rings. This leads towards a systematic study of the class of ordered fields whic…
Value Groups and Residue Fields of Models of Real Exponentiation
Lothar Sebastian Krapp
Let be an archimedean field, a divisible ordered abelian group and a group exponential on . A triple is realised in a non-archimedean exponential field $(K…
Models of true arithmetic are integer parts of nice real closed fields
Merlin Carl
Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that eac…