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Algebra universalis

, 79:43 | Cite as

Infinitely many reducts of homogeneous structures

  • Bertalan Bodor
  • Peter J. Cameron
  • Csaba Szabó
Article
Part of the following topical collections:
  1. In memory of E. Tamás Schmidt

Abstract

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.

Keywords

Homogeneous structure Reduct Closed subgroup of automorphisms 

Mathematics Subject Classification

03C07 20B27 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Bertalan Bodor
    • 1
  • Peter J. Cameron
    • 2
  • Csaba Szabó
    • 1
  1. 1.Department of Algebra and Number TheoryEötvös Loránd UniversityBudapestHungary
  2. 2.School of Mathematics and StatisticsUniversity of St AndrewsFifeUK

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