Comparison of exponential‐logarithmic and logarithmic‐exponential series
Copyright policy )Comparison of exponential‐logarithmic and logarithmic‐exponential series
AbstractWe explain how the field of logarithmic‐exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential‐logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential‐logarithmic series embeds in the field of logarithmic‐exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non‐isomorphic models of Th\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(\mathbb {R}_{\mbox{an, exp}})$\end{document}; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
- University of Salford United Kingdom
- University of Konstanz Germany
Ordered fields, Morphisms of prelogarithmic fields, non-archimedean models, Growth axioms, Model-theoretic algebra, Exponential closure, Formal power series rings, Valuations and their generalizations for commutative rings, generalized power series, Mathematics - Logic, exponential field, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Exponential extension, FOS: Mathematics, Generalized power series, Hahn groups, ordered field, Logic (math.LO), Valued fields, Model theory of fields, real exponentiation
Ordered fields, Morphisms of prelogarithmic fields, non-archimedean models, Growth axioms, Model-theoretic algebra, Exponential closure, Formal power series rings, Valuations and their generalizations for commutative rings, generalized power series, Mathematics - Logic, exponential field, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Exponential extension, FOS: Mathematics, Generalized power series, Hahn groups, ordered field, Logic (math.LO), Valued fields, Model theory of fields, real exponentiation
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!