Abstract
In PA we can define the concept of feasible interpretability. Informally stated, U feasibly interprets V iff:
for some interpretation, U proves the interpretations of all axioms of V by proofs with Gödel numbers of length polynomial in the length of the Gödel numbers of those axioms.
We prove that there is a Σ 01 -formula ξ such that
{e | PA feasibly interprets PA + ξ(ē)}
is Σ 02 -complete. The method of proof that we use combines a recursion-theoretical reduction and an adaptation of some lemmas from Lindström’s paper [5].
Research supported by the Netherlands Organization for Scientific Research (NWO).
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© 1995 Birkhäuser Boston
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Verbrugge, R. (1995). The Complexity of Feasible Interpretability. In: Clote, P., Remmel, J.B. (eds) Feasible Mathematics II. Progress in Computer Science and Applied Logic, vol 13. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2566-9_15
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DOI: https://doi.org/10.1007/978-1-4612-2566-9_15
Publisher Name: Birkhäuser Boston
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