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Asymptotic density in quasi-logarithmic additive number systems


Nietlispach, Bruno (2008). Asymptotic density in quasi-logarithmic additive number systems. Mathematical Proceedings of the Cambridge Philosophical Society, 144(2):267-287.

Abstract

We show that in quasi-logarithmic additive number systems $\mycal{A}$ all partition sets have asymptotic density, and we obtain a corresponding monadic second-order limit law for adequate classes of relational structures. Our conditions on the local counting function p(n) of the set of irreducible elements of $\mycal{A}$ allow situations which are not covered by the density theorems of Compton [6] and Woods [15]. We also give conditions on p(n) which are sufficient to show the assumptions of Compton's result are satisfied, but which are not necessarily implied by those of Bell and Burris [2], Granovsky and Stark [8] or Stark [14]

Abstract

We show that in quasi-logarithmic additive number systems $\mycal{A}$ all partition sets have asymptotic density, and we obtain a corresponding monadic second-order limit law for adequate classes of relational structures. Our conditions on the local counting function p(n) of the set of irreducible elements of $\mycal{A}$ allow situations which are not covered by the density theorems of Compton [6] and Woods [15]. We also give conditions on p(n) which are sufficient to show the assumptions of Compton's result are satisfied, but which are not necessarily implied by those of Bell and Burris [2], Granovsky and Stark [8] or Stark [14]

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:1 March 2008
Deposited On:23 Oct 2018 17:01
Last Modified:26 Jan 2022 17:39
Publisher:Cambridge University Press
ISSN:0305-0041
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s0305004107000862

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