Results 11 to 20 of about 94,120 (308)
Ordered Rings and Fields [PDF]
Formalized Mathematics, 2017 Summary We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9].
Christoph Schwarzweller +1 more
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Ordered transexponential fields
Annals of Pure and Applied Logic, 2023 26 pages, including 2 ...
Krapp, Lothar Sebastian, Kuhlmann, Salma
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On definable completeness for ordered fields [PDF]
Reports on Mathematical Logic, 2019 We show that there are 0-definably complete ordered fields which are not real closed. Therefore, the theory of definably with parameters complete ordered fields does not follow from the theory of 0-definably complete ordered fields. The mentioned completeness notions for ordered fields are the definable versions of completeness in the sense of Dedekind
Moniri, Mojtaba
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Completeness of Ordered Fields and a Trio of Classical Series Tests [PDF]
Abstract and Applied Analysis, 2016 This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field. It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field;
Robert Kantrowitz, Michael M. Neumann
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*-valuations and ordered *-fields [PDF]
Transactions of the American Mathematical Society, 1980 We generalize elementary valuation theory to *-fields (division rings with involution), apply the generalized theory to the task of ordering *-fields, and give some applications to Hermitian forms.
Samuel S. Holland
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Journal of Combinatorial Theory, Series A, 1973 AbstractWe introduce the abstract notion of an ordered differential field and show that some of the basic asymptotic growth properties of differentiable functions can be discussed within this setting. However, in order to ensure that log x → ∞ as x → ∞, we have to assume that the field of constants is archimedean.
Robinson, Abraham
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Polarization of Intrabinary Shock Emission in Spider Pulsars
The Astrophysical Journal, 2023 In so-called spider pulsars, the X-ray band is dominated by intrabinary shock (IBS) synchrotron emission. While the double-peaked X-ray light curves from these shocks have been well characterized in several spider systems (both black widows and redbacks),
Andrew G. Sullivan, Roger W. Romani
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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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New Journal of Physics, 2022 Pyrochlores offer an ideal playground to investigate the magnetic ground state of frustrated magnetic systems. In this class of materials, competition between various magnetic interactions remains frustrated and prevents an ordered magnetic state at low ...
Karan Singh +3 more
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Definable valuations on ordered fields
, 2022 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}_ ...
Krapp, Lothar Sebastian +4 more
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