Source: J. Symbolic Logic
Volume 72, Issue 3
Let T be a recursive theory in the language of first order Arithmetic. We
prove that if T extends: (a) the scheme of
parameter free Δ1-minimization (plus exp), or (b) the scheme of
parameter free Π1-induction, then there are no Σ1-maximal
models with respect to T. As a consequence, we obtain a new proof of an
unpublished theorem of Jeff Paris stating that Σ1-maximal models
with respect to IΔ0 + exp do not satisfy the scheme of
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