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Displaying similar documents to “On a system of axioms which has no recursively enumerable arithmetic model”

An application of a reflection principle

Zofia Adamowicz, Leszek Aleksander Kołodziejczyk, Paweł Zbierski (2003)

Fundamenta Mathematicae

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We define a recursive theory which axiomatizes a class of models of IΔ₀ + Ω ₃ + ¬ exp all of which share two features: firstly, the set of Δ₀ definable elements of the model is majorized by the set of elements definable by Δ₀ formulae of fixed complexity; secondly, Σ₁ truth about the model is recursively reducible to the set of true Σ₁ formulae of fixed complexity.