The finitely axiomatizable complete theories of non-associative arrow frames

Khaled M. K. M. I.

Advances in Mathematics, cilt.346, ss.194-218, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 346
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.aim.2019.01.014
  • Dergi Adı: Advances in Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.194-218
  • Anahtar Kelimeler: Arrow logic, Finitely axiomatizable theories, Relation algebras
  • İstanbul Medipol Üniversitesi Adresli: Hayır

Özet

Arrow logic is a modal logic that is designed to talk about objects that can be illustrated as arrows. In this article, we consider the non-associative arrow logic NAL. We list all the finitely axiomatizable, complete and consistent theories of NAL. This gives an answer to the open problem, posed by I. Németi, addressing the atomicity of the free algebras of the class NA of non-associative relation algebras. We use the method of games as introduced to the fields of logic and algebra by R. Hirsch and I. Hodkinson. We also give a simple proof for the known fact that NAL is decidable through the finite model property.