Expansions of the group of integers by Beatty sequences

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GÜNAYDIN A., Özsahakyan M.

Annals of Pure and Applied Logic, cilt.173, sa.3, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 173 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.apal.2021.103062
  • Dergi Adı: Annals of Pure and Applied Logic
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Periodicals Index Online, INSPEC, MathSciNet, Philosopher's Index, zbMATH
  • Anahtar Kelimeler: Beatty sequences, dp-minimal, Expansions of integers
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

We study the model theoretic structure (Z,+,Pr) where r>1 is an irrational number and the elements of Pr are of the form ⌊nr⌋ for some n∈Z∖{0}. We axiomatize this structure and prove a quantifier elimination result. As a consequence, we get that definable subsets are not sparse unless they are finite. We also prove that there are no reducts of this structure expanding (Z,+).