First order logic without equality on relativized semantics

Banerjee A., Khaled M. K. M. I.

Annals of Pure and Applied Logic, cilt.169, sa.11, ss.1227-1242, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 169 Sayı: 11
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.apal.2018.07.002
  • Dergi Adı: Annals of Pure and Applied Logic
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1227-1242
  • Anahtar Kelimeler: Atoms, Free algebras, Zero-dimensional elements
  • İstanbul Medipol Üniversitesi Adresli: Hayır

Özet

Let α≥2 be any ordinal. We consider the class Drsα of relativized diagonal free set algebras of dimension α. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of Drsα are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class Drsα corresponds to first order logic, without equality symbol, with α-many variables and on relativized semantics. Hence, in this variation of first order logic, there is no finitely axiomatizable, complete and consistent theory.