, Volume 39, Issue 4, pp 347-354

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

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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.