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Algebra universalis

, 80:21 | Cite as

Small inductive dimension and universality on frames

  • Dimitrios N. GeorgiouEmail author
  • Stavros D. Iliadis
  • Athanasios C. Megaritis
  • Fotini Sereti
Article
  • 25 Downloads

Abstract

In this paper we prove that for a fixed integer or an ordinal \(\alpha \) and a fixed infinite cardinal \(\tau \) the class of all regular frames of weight less than or equal to \(\tau \) with small inductive dimension less than or equal to \(\alpha \) is saturated and therefore, in this class of frames there exist universal elements.

Keywords

Small inductive dimension of frames Universal frame Saturated class of frames 

Mathematics Subject Classification

06A06 06D22 06F30 54H12 54F05 

Notes

Acknowledgements

The authors would like to thank the referee for the careful reading of the paper and the useful comments. The fourth author of the paper F. Sereti (with scholarship code 2547) would like to thank the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI) for the financial support of this study.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dimitrios N. Georgiou
    • 1
    Email author
  • Stavros D. Iliadis
    • 2
  • Athanasios C. Megaritis
    • 3
  • Fotini Sereti
    • 1
  1. 1.Department of MathematicsUniversity of PatrasPatrasGreece
  2. 2.Department of General Topology and GeometryMoscow State University (M. V. Lomonosov)MoscowRussia
  3. 3.Department of Computer EngineeringTechnological Educational Institute of PeloponneseSpartaGreece

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