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1.
Downey Rodney G.; Lempp Steffen; Shore Richard A. 《Journal London Mathematical Society》1996,54(3):417-439
We show that there is a degree a REA in and low over 0' suchthat no minimal degree below 0' jumps to a degree above a. Wealso show that every nonlow recursively enumerable degree boundsa nonlow minimal degree. 相似文献
2.
3.
We study the set of depths of relative algebras of countable Boolean algebras, in particular the extent to which this set may not be downward closed within the countable ordinals for a fixed countable Boolean algebra. Doing so, we exhibit a structural difference between the class of arbitrary rank countable Boolean algebras and the class of rank one countable Boolean algebras. 相似文献
4.
We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut
c
(Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut
c
(Q). Also, Aut(Q) has three fundamental properties which fail in Aut
c
(Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures. 相似文献
5.
Steffen Lempp André Nies Theodore A. Slaman 《Transactions of the American Mathematical Society》1998,350(7):2719-2736
We show the undecidability of the -theory of the partial order of computably enumerable Turing degrees.
6.
We show that any
-initial segment of a recursive linear order can be presented recursively. 相似文献
7.
A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices. 相似文献
8.
Ambos-Spies Klaus; Lempp Steffen; Lerman Manuel 《Journal London Mathematical Society》1994,49(1):1-15
We show that a finite distributive lattice can be embedded intothe r.e. degrees preserving least and greatest element if andonly if the lattice contains a join-irreducible noncappableelement. 相似文献
9.
We show the existence of a high r. e. degree bounding only joins of minimal pairs and of a high2 nonbounding r. e. degree. MSC: 03D25. 相似文献
10.
We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0
3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
Received: 6 November 1999 / Revised version: 10 March 2000 /?Published online: 18 May 2001 相似文献