Studia Logica: An International Journal for Symbolic Logic, Vol. 106, No. 2 (April 2018), pp. 219-235 (17 pages) We prove that for any recursively axiomatized consistent extension of Peano Arithmetic, ...

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Let L be a positive, linear functional and F be an approximation to L that is exact for polynomials of degree n - 1. According to Peano's theorem we can write (L - F)(f) = R(f) = ∫ f (n) (t)K(t) dt, ...