Abstract
For every sequence ϕ ≡ |p n } n∈ω of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory ℐ diagonalizable algebras, we associate a formulaϕ 0 A, called “the value ofA inPA with respect to the interpretationϕ.”
We show that, ifA is true in every diagonalizable algebra, then, for everyϕ, ϕ 0 A is a theorem ofPA.
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Montagna, F. Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic. Stud Logica 39, 347–354 (1980). https://doi.org/10.1007/BF00713544
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DOI: https://doi.org/10.1007/BF00713544