9 papers
Algorithmic Construction of Real Hyperfields from Minimal Axioms
Dawid E. Kędzierski, Katarzyna Kuhlmann, Hanna Stojałowska
We study real hyperfields, focusing in particular on those that are finite with cyclic positive cones. All real hyperfields have characteristic zero, although they can still be cla…
Arithmetic of cuts in ordered abelian groups and of ideals over valuation rings
Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
We investigate existence, uniqueness and maximality of solutions for equations and inequalities where and are final segments of ord…
Orderings and valuations in hyperfields
Katarzyna Kuhlmann, Alessandro Linzi, Hanna Stojałowska
We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induc…
Density of Composite Places in Function Fields and Applications to Real Holomorphy Rings
Eberhard Becker, Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
Given an algebraic function field and a place on , we prove that the places that are composite with extensions of to finite extensions of lie dense in the…
A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures
Hanna Ćmiel, Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordere…
Construction of ball spaces and the notion of continuity
René Bartsch, Katarzyna Kuhlmann, Franz-Viktor Kuhlmann
Spherically complete ball spaces provide a framework for the proof of generic fixed point theorems. For the purpose of their application it is important to have methods for the con…
Places, cuts and orderings of function fields
Przemysław Koprowski, Katarzyna Kuhlmann
In this paper we investigate the space of -places of an algebraic function field of one variable. We deal with the problem of determining when two orderings of such a f…
Embedding theorems for spaces of -places of rational function fields and their products
Franz-Viktor Kuhlmann, Katarzyna Kuhlmann
We study spaces of -places of rational function fields in one variable. For extensions of formally real fields, with real closed and satisfying a nat…
A common generalization of metric, ultrametric and topological fixed point theorems - alternative version
Katarzyna Kuhlmann, Franz-Viktor Kuhlmann
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixe…