2 Leo Harrington And
نویسنده
چکیده
1. Introduction A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements.
منابع مشابه
The d . r . e . degrees are not dense S . BARRY COOPER LEO HARRINGTON ALISTAIR H . LACHLAN STEFFEN LEMPP
By constructing a maximal inco1nplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees (n 2 2) and of the w-r.e, degrees,
متن کاملHarrington’s results on arithmetical singletons
We exposit two previously unpublished results due to Leo Harrington. The first result says that there exist arithmetical singletons which are arithmetically incomparable. The second result says that there exists a ranked point which is not an arithmetical singleton.
متن کاملThere is No Fat Orbit
We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.
متن کاملHarrington's conservation theorem redone
Leo Harrington showed that the second-order theory of arithmetic WKL0 is Π 1 -conservative over the theory RCA0. Harrington’s proof is modeltheoretic, making use of a forcing argument. A purely proof-theoretic proof, avoiding forcing, has been eluding the efforts of researchers. In this short paper, we present a proof of Harrington’s result using a cut-elimination argument.
متن کاملIsomorphisms of splits of computably enumerable sets
We show that if A and  are automorphic via 8 then the structures SR(A) and SR( Â) are 13-isomorphic via an isomorphism 9 induced by 8. Then we use this result to classify completely the orbits of hhsimple sets.
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تاریخ انتشار 1996