{"title":"两个连续数上可除谓词的几个可判定性和可定义性问题","authors":"M. Starchak","doi":"10.32603/2071-2340-2018-6-5-15","DOIUrl":null,"url":null,"abstract":"The predicate of divisibility on two consecutive numbers DW(x,y) ÷ x | y ∧ 1+x | y was introduced by L. van den Dries and A. Wilkie when they studied some properties of subsets of natural numbers, existentially definable with unit, addition and divisibility. Undecidability of the existential theory of natural numbers with multiplication and DW and definability of addition and multiplication in terms of DWand divisibility is proved in the paper. Then the definability of multiplication in the terms of addition and DW is proved. Some definability questions for order and DW are also considered in the paper.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"53 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some Decidability and Definability Problems for the Predicate of the Divisibility on Two Consecutive Numbers\",\"authors\":\"M. Starchak\",\"doi\":\"10.32603/2071-2340-2018-6-5-15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The predicate of divisibility on two consecutive numbers DW(x,y) ÷ x | y ∧ 1+x | y was introduced by L. van den Dries and A. Wilkie when they studied some properties of subsets of natural numbers, existentially definable with unit, addition and divisibility. Undecidability of the existential theory of natural numbers with multiplication and DW and definability of addition and multiplication in terms of DWand divisibility is proved in the paper. Then the definability of multiplication in the terms of addition and DW is proved. Some definability questions for order and DW are also considered in the paper.\",\"PeriodicalId\":319537,\"journal\":{\"name\":\"Computer Tools in Education\",\"volume\":\"53 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Tools in Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32603/2071-2340-2018-6-5-15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Tools in Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32603/2071-2340-2018-6-5-15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
两个连续数DW(x,y) ÷ x | y∧1+x | y的可整除性谓词是由L. van den Dries和A. Wilkie在研究具有单位、加法和可整除性存在可定义的自然数子集的一些性质时引入的。证明了具有乘法和DW的自然数存在论的不确定性，以及加法和乘法在DW可整除性方面的可定义性。然后证明了乘法在加法和DW方面的可定义性。本文还讨论了订单和DW的一些可定义性问题。
Some Decidability and Definability Problems for the Predicate of the Divisibility on Two Consecutive Numbers
The predicate of divisibility on two consecutive numbers DW(x,y) ÷ x | y ∧ 1+x | y was introduced by L. van den Dries and A. Wilkie when they studied some properties of subsets of natural numbers, existentially definable with unit, addition and divisibility. Undecidability of the existential theory of natural numbers with multiplication and DW and definability of addition and multiplication in terms of DWand divisibility is proved in the paper. Then the definability of multiplication in the terms of addition and DW is proved. Some definability questions for order and DW are also considered in the paper.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
