On b Q 1 $bQ_1$ -degrees of c.e. sets

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-11-20 DOI:10.1002/malq.202300033

Roland Omanadze, Irakli Chitaia

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引用次数: 0

Abstract

Using properties of simple sets we study ${b Q}_{1}$ -degrees of c.e. sets. In particular, we prove: (1) If $A$ and $B$ are c.e. sets, $A$ is a simple set and $A \leq_{{b Q}_{1}} B$ , then there exists a simple set $C$ such that $C \leq_{1} A$ and $C \leq_{1} B$ . (2) the c.e. ${b Q}_{1}$ -degrees ( ${b Q}_{1}$ -degrees) do not form an upper semilattice. (3) The c.e. ${b Q}_{1}$ -degrees are not dense, but are upwards dense. (4) The ${b Q}_{1}$ -degrees are not dense.

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在bQ1$bQ_1$- c集合的度数上

利用简单集的性质研究了c.e.集的bQ1${bQ}_1$-度。特别地，我们证明了:(1)如果A和B是c.e.集合，A是一个简单集合，且A≤bQ1B$A\le _{{bQ}_{1}}B$，则存在一个简单集合C，使得C≤1A$C\le _1 A$且C≤1B$C\le _1 B$。(2) c.e. bQ1${bQ}_1$-degrees (bQ1${bQ}_1$-degrees)不构成上半格。(3) c.e. bQ1${bQ}_1$-度不致密，但向上致密。(4) bQ1${bQ}_1$-度不密集。

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.