一阶逻辑的不动点扩展

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI:10.1109/SFCS.1985.27

Y. Gurevich, S. Shelah

{"title":"一阶逻辑的不动点扩展","authors":"Y. Gurevich, S. Shelah","doi":"10.1109/SFCS.1985.27","DOIUrl":null,"url":null,"abstract":"We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"292","resultStr":"{\"title\":\"Fixed-point extensions of first-order logic\",\"authors\":\"Y. Gurevich, S. Shelah\",\"doi\":\"10.1109/SFCS.1985.27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.\",\"PeriodicalId\":296739,\"journal\":{\"name\":\"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)\",\"volume\":\"95 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"292\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1985.27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1985.27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 292

摘要

我们分别用正归纳、单调归纳和所谓的非单调(在我们的术语中称为膨胀)归纳证明了一阶逻辑的三种扩展在有限结构下都具有相同的表达能力。作为一个副产品，可以推导出相应的定点层次的崩溃。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fixed-point extensions of first-order logic

We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

26th Annual Symposium on Foundations of Computer Science (sfcs 1985)

自引率

0.00%

发文量