Logic, Computation, Hierarchies最新文献_第2页

On the strongly bounded turing degrees of simple sets 关于简单集的强有界图灵度

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.23

K. Ambos-Spies

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引用次数: 0

An Isomorphism Theorem for Partial Numberings 部分数的一个同构定理

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.341

D. Spreen

{"title":"An Isomorphism Theorem for Partial Numberings","authors":"D. Spreen","doi":"10.1515/9781614518044.341","DOIUrl":"https://doi.org/10.1515/9781614518044.341","url":null,"abstract":"As has been shown by the author, standard numberings of the computable real numbers and similar effectively given topological spaces are only partially defined, by necessity. Thus, not every natural number is a name of some computable object. It was demonstrated that any two such numberings are m-equivalent. Spaces like the partial computable functions, on the other hand, are known to have totally defined standard numberings such that any two of them are even recursively isomorphic. In this paper it is studied whether such a result is also true for standard numberings of the computable reals and similar spaces. The investigation is carried out in the general setting of effective topological spaces introduced in earlier papers of the author. For total numberings it is well known that m-equivalent numberings are recursively isomorphic if they are precomplete. The proof proceeds in two steps: First it is shown that m-equivalent precomplete numberings are already 1-equivalent and then a generalization of Myhill’s theorem is applied. If one extends the usual reducibility relation between numberings to partial numberings in a straightforward way, the reduction function is allowed to map non-names with respect to one numbering onto names with respect to the other. A recursive isomorphism, however, can only map non-names onto non-names. If one allows only reduction functions operating in the same way—we speak of strong reducibility in this case—, the usual construction for Myhill’s theorem goes through and one obtains a generalization of this theorem to partial numberings. A numbering is precomplete if every partial computable index function can be totalized relative to the numbering. We call it strongly precomplete in case there is always a totalizer with the property that if the value of the partial index function is a non-name, the same is true for the corresponding value of the totalizer. It is shown in this case that any numbering being strongly m-reducible to the given numbering is in fact strongly 1-reducible to it. In the second part of the paper the notion of admissible numbering of an effective space is strengthened in a similar way as were the notions of reducibility and precompleteness. For the strongly admissible numberings thus obtained one has that any two of them are even strongly m-equivalent. A necessary and sufficient condition is presented for when such numberings are strongly precompete. As is shown, effective spaces have strongly admissible, strongly precomplete numberings. By the above results any two of them are recursively isomorphic.","PeriodicalId":359337,"journal":{"name":"Logic, Computation, Hierarchies","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129114981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Tight extensions of T T的紧密延伸

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.9

C. A. Agyingi, P. Haihambo, H. Künzi

引用次数: 0

The life and work of Victor L. Selivanov 维克多·l·塞利万诺夫的生活和工作

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.1

D. Spreen

引用次数: 0

Partial Numberings and Precompleteness 部分编号和预完备性

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.325

D. Spreen

引用次数: 1

An Approach to Design of Automata-Based Axiomatization for Propositional Program and Temporal Logics (by Example of Linear Temporal Logic) 基于自动机的命题程序和时间逻辑公理化设计方法(以线性时间逻辑为例)

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.297

N. Shilov

引用次数: 4

Some Notes on the Universality of Three-Orders on Finite Labeled Posets 有限标记偏序集上三阶普遍性的若干注记

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.393

Anton V. Zhukov

引用次数: 1

Two Theorems on the Hausdorff Measure of Regular ω-Languages 正则ω-语言的Hausdorff测度的两个定理

Logic, Computation, Hierarchies Pub Date : 1900-01-01 DOI: 10.1515/9781614518044.383

L. Staiger

引用次数: 1