Amalgamation and Robinson property in universal algebraic logic

Gyenis Z., Öztürk Ö.

Logic Journal of the IGPL, vol.32, no.1, pp.180-196, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1093/jigpal/jzac076
  • Journal Name: Logic Journal of the IGPL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.180-196
  • Keywords: Amalgamation, Beth property, interpolation property, Robinson consistency, strong amalgamation
  • Yozgat Bozok University Affiliated: No

Abstract

There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also shown that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation.