Interpreting Arithmetic in the R.e. Degrees under 4-induction
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چکیده
We study the problem of the interpretability of arithmetic in the r.e. degrees in models of fragments of Peano arithmetic. The main result states that there is an interpretation φ 7→ φ∗ such that every formula φ of Peano arithmetic corresponds to a formula φ∗ in the language of the partial ordering of r.e. degrees such that for every model N of Σ4-induction, N |= φ if and only if RN |= φ∗, whereRN is the structure whose universe is the collection of r.e. degrees inN . This supplies, for example, statements φm about the r.e. degrees which are equivalent (over IΣ4) to IΣm for every m > 4. §
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تاریخ انتشار 2000