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We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ
-set of reals in Lebesgue measurable+every Π
-set of reals isK
σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ
-sets of reals is Lebesgue measurable, has...
We interpret intuitionistic theories of (iterated) strictly positive inductive definitions (s.p.-ID
s) into Martin-Löf's type theory. The main purpose being to obtain lower bounds of the proof-theoretic strength of type theories furnished with means for transfinite induction (W-type, Aczel's...
Fragments of extensional Martin-Löf type theory without universes,ML
0, are introduced that conservatively extend S.A. Cook and A. Urquhart'sIPV
ω. A model for these restricted theories is obtained by interpretation in Feferman's theory APP of operators, a natural model of which is the class of...
In this paper we investigate problems about densities ofe-generic,s-generic andp-generic degrees. We, in particular, show that allp-generic degrees are non-branching, which answers an open question by Jockusch who asked: whether alls-generic degrees are non-branching and refutes a conjecture of...
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