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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 64, Issue 3


A note on the convexity of lattices generated by the set of nonnegative integers

Jozef Pócs
  • Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia
  • Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic
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Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0225-7


A class of lattices is said to be a convexity if it is closed under homomorphic images, convex sublattices and direct products. The main aim of this paper is to show that convexity generated by nonnegative integers contains all ordinal numbers. Consequently, any two infinite ordinals generate the same convexity.

MSC: Primary 06B99

Keywords: lattice; convexity; ultraproduct

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 555–562, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0225-7.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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