{"title":"Remarks on simple proofs","authors":"Rosalie Iemhoff","doi":"10.1007/978-3-319-53385-8_12","DOIUrl":"https://doi.org/10.1007/978-3-319-53385-8_12","url":null,"abstract":"","PeriodicalId":161799,"journal":{"name":"Logic group preprint series","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121435413","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}
Vedran Cacic, Pavel Pudlák, Greg Restall, A. Urquhart, Albert Visser
{"title":"Decorated linear order types and the theory of concatenation","authors":"Vedran Cacic, Pavel Pudlák, Greg Restall, A. Urquhart, Albert Visser","doi":"10.1017/CBO9780511778421.003","DOIUrl":"https://doi.org/10.1017/CBO9780511778421.003","url":null,"abstract":"We study the interpretation of Grzegorczyk’s Theory of Concatenation \u0000TC in structures of decorated linear order types satisfying Grzegorczyk’s \u0000axioms. We show that TC is incomplete for this interpretation. What \u0000is more, the first order theory validated by this interpretation interprets \u0000arithmetical truth. We also show that every extension of TC has a model \u0000that is not isomorphic to a structure of decorated order types. \u0000We provide a positive result, to wit a construction that builds structures \u0000of decorated order types from models of a suitable concatenation \u0000theory. This construction has the property that if there is a representation \u0000of a certain kind, then the construction provides a representation of \u0000that kind.","PeriodicalId":161799,"journal":{"name":"Logic group preprint series","volume":"26 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125741837","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}
{"title":"Extension and Interpretability","authors":"A. Visser","doi":"10.1007/978-3-030-53654-1_3","DOIUrl":"https://doi.org/10.1007/978-3-030-53654-1_3","url":null,"abstract":"","PeriodicalId":161799,"journal":{"name":"Logic group preprint series","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125207701","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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