We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin (11). We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are@0 -categorical and@0 -stable. In particular they are stable. 2000 Mathematics Subject Classification 03C98 (primary); 46E30 (secondary)
{"title":"Modular functionals and perturbations of Nakano spaces","authors":"I. Yaacov","doi":"10.4115/jla.2009.1.1","DOIUrl":"https://doi.org/10.4115/jla.2009.1.1","url":null,"abstract":"We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin (11). We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are@0 -categorical and@0 -stable. In particular they are stable. 2000 Mathematics Subject Classification 03C98 (primary); 46E30 (secondary)","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2008-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70874988","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}
Pub Date : 2008-02-18DOI: 10.1007/s11813-007-0005-6
Robert S. Lubarsky, M. Rathjen
{"title":"On the constructive Dedekind reals","authors":"Robert S. Lubarsky, M. Rathjen","doi":"10.1007/s11813-007-0005-6","DOIUrl":"https://doi.org/10.1007/s11813-007-0005-6","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"24 1","pages":"131-152"},"PeriodicalIF":0.2,"publicationDate":"2008-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73192321","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}
Pub Date : 2008-02-18DOI: 10.1007/s11813-007-0004-7
T. Lindstrøm
{"title":"Nonlinear stochastic integrals for hyperfinite Lévy processes","authors":"T. Lindstrøm","doi":"10.1007/s11813-007-0004-7","DOIUrl":"https://doi.org/10.1007/s11813-007-0004-7","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"257 1","pages":"91-129"},"PeriodicalIF":0.2,"publicationDate":"2008-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75956718","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}
Pub Date : 2008-01-01DOI: 10.1007/s11813-008-0009-x
Itaï Ben Yaacov
{"title":"Topometric spaces and perturbations of metric structures","authors":"Itaï Ben Yaacov","doi":"10.1007/s11813-008-0009-x","DOIUrl":"https://doi.org/10.1007/s11813-008-0009-x","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"22 1","pages":"235-272"},"PeriodicalIF":0.2,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80488900","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}
Pub Date : 2007-12-17DOI: 10.1007/s11813-008-0008-y
T. Todorov, H. Vernaeve
{"title":"Full algebra of generalized functions and non-standard asymptotic analysis","authors":"T. Todorov, H. Vernaeve","doi":"10.1007/s11813-008-0008-y","DOIUrl":"https://doi.org/10.1007/s11813-008-0008-y","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"80 1","pages":"205-234"},"PeriodicalIF":0.2,"publicationDate":"2007-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91024616","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}
Pub Date : 2007-09-24DOI: 10.1007/s11813-007-0003-8
N. Cutland
{"title":"Introducing Logic and Analysis","authors":"N. Cutland","doi":"10.1007/s11813-007-0003-8","DOIUrl":"https://doi.org/10.1007/s11813-007-0003-8","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"5 1","pages":"v"},"PeriodicalIF":0.2,"publicationDate":"2007-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90638106","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}
Pub Date : 2007-09-24DOI: 10.1007/s11813-007-0002-9
Renling Jin
{"title":"Inverse problem for cuts","authors":"Renling Jin","doi":"10.1007/s11813-007-0002-9","DOIUrl":"https://doi.org/10.1007/s11813-007-0002-9","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"31 1","pages":"61-89"},"PeriodicalIF":0.2,"publicationDate":"2007-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86652343","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}
Pub Date : 2006-04-16DOI: 10.1007/s11813-007-0001-x
Lars Brünjes, C. Serpé
{"title":"Enlargements of schemes","authors":"Lars Brünjes, C. Serpé","doi":"10.1007/s11813-007-0001-x","DOIUrl":"https://doi.org/10.1007/s11813-007-0001-x","url":null,"abstract":"","PeriodicalId":53872,"journal":{"name":"Journal of Logic and Analysis","volume":"10 1","pages":"1-60"},"PeriodicalIF":0.2,"publicationDate":"2006-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87412221","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}
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