准时编号的罗杰斯半格

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2022-02-01 DOI:10.1017/S0960129522000093
N. Bazhenov, M. Mustafa, S. Ospichev
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引用次数: 0

摘要

摘要本文在准时可计算性的框架内工作,重点是消除代数和无限组合数学中构造的无界搜索。我们研究了准时数,即原始递归函数族S的一致计算。数之间的准时可约性是由原始递归函数引起的。这种方法产生了度的上半格,称为Rogers-pr半格。我们证明了任何无穷的一致原始递归族S都会诱导一个无穷的Rogers-pr半格R。我们证明了半格R不具有极小元素,并且R内的每个非平凡区间都包含一个无穷反链。此外,来自R的每个非最大元素都是无限反链的一部分。我们证明了Th(R)理论的$\ Sigma_1$-片段是可判定的。
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Rogers semilattices of punctual numberings
Abstract The paper works within the framework of punctual computability, which is focused on eliminating unbounded search from constructions in algebra and infinite combinatorics. We study punctual numberings, that is, uniform computations for families S of primitive recursive functions. The punctual reducibility between numberings is induced by primitive recursive functions. This approach gives rise to upper semilattices of degrees, which are called Rogers pr-semilattices. We show that any infinite, uniformly primitive recursive family S induces an infinite Rogers pr-semilattice R. We prove that the semilattice R does not have minimal elements, and every nontrivial interval inside R contains an infinite antichain. In addition, every non-greatest element from R is a part of an infinite antichain. We show that the $\Sigma_1$ -fragment of the theory Th(R) is decidable.
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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