{"title":"关于L p格和其他度量结构中的一致正则基","authors":"I. Yaacov","doi":"10.4115/JLA.2012.4.12","DOIUrl":null,"url":null,"abstract":"We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless Lp lattices. We also discuss the connection between the definability of the set of uniform canonical bases and the existence of the theory of beautiful pairs (i.e., with the finite cover property), and prove in particular that the set of uniform canonical bases is definable in algebra- ically closed metric valued fields. 2010 Mathematics Subject Classification 03C45 (primary); 46B42,12J25 (second- ary)","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"4 1","pages":"1-30"},"PeriodicalIF":0.3000,"publicationDate":"2010-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"On uniform canonical bases in L p lattices and other metric structures\",\"authors\":\"I. Yaacov\",\"doi\":\"10.4115/JLA.2012.4.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless Lp lattices. We also discuss the connection between the definability of the set of uniform canonical bases and the existence of the theory of beautiful pairs (i.e., with the finite cover property), and prove in particular that the set of uniform canonical bases is definable in algebra- ically closed metric valued fields. 2010 Mathematics Subject Classification 03C45 (primary); 46B42,12J25 (second- ary)\",\"PeriodicalId\":53872,\"journal\":{\"name\":\"Journal of Logic and Analysis\",\"volume\":\"4 1\",\"pages\":\"1-30\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2010-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logic and Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4115/JLA.2012.4.12\",\"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.2012.4.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
On uniform canonical bases in L p lattices and other metric structures
We discuss the notion of uniform canonical bases, both in an abstract manner and specifically for the theory of atomless Lp lattices. We also discuss the connection between the definability of the set of uniform canonical bases and the existence of the theory of beautiful pairs (i.e., with the finite cover property), and prove in particular that the set of uniform canonical bases is definable in algebra- ically closed metric valued fields. 2010 Mathematics Subject Classification 03C45 (primary); 46B42,12J25 (second- ary)
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"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.
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