Pub Date : 1900-01-01DOI: 10.1007/978-3-319-53385-8_12
Rosalie Iemhoff
{"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}
Pub Date : 1900-01-01DOI: 10.1017/CBO9780511778421.003
Vedran Cacic, Pavel Pudlák, Greg Restall, A. Urquhart, Albert Visser
We study the interpretation of Grzegorczyk’s Theory of Concatenation TC in structures of decorated linear order types satisfying Grzegorczyk’s axioms. We show that TC is incomplete for this interpretation. What is more, the first order theory validated by this interpretation interprets arithmetical truth. We also show that every extension of TC has a model that is not isomorphic to a structure of decorated order types. We provide a positive result, to wit a construction that builds structures of decorated order types from models of a suitable concatenation theory. This construction has the property that if there is a representation of a certain kind, then the construction provides a representation of that kind.
{"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}
Pub Date : 1900-01-01DOI: 10.1007/978-3-030-53654-1_3
A. Visser
{"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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