Studia Logica

, Volume 39, Issue 4, pp 347–354

Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

  • Franco Montagna

DOI: 10.1007/BF00713544

Cite this article as:
Montagna, F. Stud Logica (1980) 39: 347. doi:10.1007/BF00713544


For every sequence ϕ ≡ |pn}n∈ω of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory ℐ diagonalizable algebras, we associate a formulaϕ0A, called “the value ofA inPA with respect to the interpretationϕ.”

We show that, ifA is true in every diagonalizable algebra, then, for everyϕ, ϕ0A is a theorem ofPA.

Copyright information

© Polish Academy of Sciences 1980

Authors and Affiliations

  • Franco Montagna
    • 1
  1. 1.Institute of MathematicsSiena UniversityItaly