{"title":"连续逻辑的广义有效完备性","authors":"Caleb Camrud","doi":"10.4115/jla.2023.15.4","DOIUrl":null,"url":null,"abstract":"In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows that any decidable theory is satisfied by a computably presentable structure. This modifies and extends previous partial effective completeness theorems for continuous logic given by Calvert and Didehvar, Ghasemloo, and Pourmahdian.","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized effective completeness for continuous logic\",\"authors\":\"Caleb Camrud\",\"doi\":\"10.4115/jla.2023.15.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows that any decidable theory is satisfied by a computably presentable structure. This modifies and extends previous partial effective completeness theorems for continuous logic given by Calvert and Didehvar, Ghasemloo, and Pourmahdian.\",\"PeriodicalId\":53872,\"journal\":{\"name\":\"Journal of Logic and Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4115/jla.2023.15.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4115/jla.2023.15.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
Generalized effective completeness for continuous logic
In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows that any decidable theory is satisfied by a computably presentable structure. This modifies and extends previous partial effective completeness theorems for continuous logic given by Calvert and Didehvar, Ghasemloo, and Pourmahdian.
期刊介绍:
"Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.