منابع مشابه
Π1 Classes with Complex Elements
An infinite binary sequence is complex if the Kolmogorov complexity of its initial segments is bounded below by a computable function. We prove that a Π01 class P contains a complex element if and only if it contains a wtt-cover for the Cantor set. That is, if and only if for every real Y there is an X in the P such that X >wtt Y . We show that this is also equivalent to the Π01 class’s being l...
متن کاملCoding true arithmetic in the Medvedev degrees of Π10 classes
Let Es denote the lattice of Medvedev degrees of non-empty Π1 subsets of 2, and let Ew denote the lattice of Muchnik degrees of non-empty Π1 subsets of 2. We prove that the first-order theory of Es as a partial order is recursively isomorphic to the first-order theory of true arithmetic. Our coding of arithmetic in Es also shows that the Σ3-theory of Es as a lattice and the Σ4-theory of Es as a...
متن کاملΠ10 classes and strong degree spectra of relations
We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear order. Countable Π1 subsets of 2 ω and Kolmogorov complexity play a major role in the proof.
متن کاملConvergence of Infinite Exponentials with Complex Elements
b-> bi where a„ = log bn. (Wherever the logarithm is used in this article it is understood to be the principal branch of the function.) However, this way of writing an infinite exponential is ambiguous since it is not clear what value of z is to be used, and since different choices of z may lead to different convergence behavior of the sequence. Instead of 2=1, we could have used 2 = 0 without ...
متن کاملDense Elements and Classes of Residuated Lattices
In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill the equation (¬ a → ¬ b) → ¬ b = (¬ b → ¬ a) → ¬ a have lifting Boolean center.
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 2008
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1230396923