Serikzhan A. Badaev, Nikolay A. Bazhenov, Birzhan S. Kalmurzayev, Manat Mustafa
{"title":"On diagonal functions for equivalence relations","authors":"Serikzhan A. Badaev, Nikolay A. Bazhenov, Birzhan S. Kalmurzayev, Manat Mustafa","doi":"10.1007/s00153-023-00896-0","DOIUrl":"https://doi.org/10.1007/s00153-023-00896-0","url":null,"abstract":"","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Compositional truth with propositional tautologies and quantifier-free correctness","authors":"Bartosz Wcisło","doi":"10.1007/s00153-023-00893-3","DOIUrl":"https://doi.org/10.1007/s00153-023-00893-3","url":null,"abstract":"Abstract In Cieśliński (J Philos Logic 39:325–337, 2010), Cieśliński asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as $$Delta _0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>Δ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with a routine argument that the principle of quantifier-free correctness is itself conservative.","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effective weak and vague convergence of measures on the real line","authors":"Diego A. Rojas","doi":"10.1007/s00153-023-00886-2","DOIUrl":"https://doi.org/10.1007/s00153-023-00886-2","url":null,"abstract":"Abstract We expand our effective framework for weak convergence of measures on the real line by showing that effective convergence in the Prokhorov metric is equivalent to effective weak convergence. In addition, we establish a framework for the study of the effective theory of vague convergence of measures. We introduce a uniform notion and a non-uniform notion of vague convergence, and we show that both these notions are equivalent. However, limits under effective vague convergence may not be computable even when they are finite. We give an example of a finite incomputable effective vague limit measure, and we provide a necessary and sufficient condition so that effective vague convergence produces a computable limit. Finally, we determine a sufficient condition for which effective weak and vague convergence of measures coincide. As a corollary, we obtain an effective version of the equivalence between classical weak and vague convergence of sequences of probability measures.","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cut elimination by unthreading","authors":"Gabriele Pulcini","doi":"10.1007/s00153-023-00892-4","DOIUrl":"https://doi.org/10.1007/s00153-023-00892-4","url":null,"abstract":"Abstract We provide a non-Gentzen, though fully syntactical, cut-elimination algorithm for classical propositional logic. The designed procedure is implemented on $$textsf{GS4}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>GS</mml:mi> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , the one-sided version of Kleene’s sequent system $$textsf{G4}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . The algorithm here proposed proves to be more ‘dexterous’ than other, more traditional, Gentzen-style techniques as the size of proofs decreases at each step of reduction. As a corollary result, we show that analyticity always guarantees minimality of the size of $$textsf{GS4}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>GS</mml:mi> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> -proofs.","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Superrosiness and dense pairs of geometric structures","authors":"Gareth J. Boxall","doi":"10.1007/s00153-023-00890-6","DOIUrl":"https://doi.org/10.1007/s00153-023-00890-6","url":null,"abstract":"Abstract Let T be a complete geometric theory and let $$T_P$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>P</mml:mi> </mml:msub> </mml:math> be the theory of dense pairs of models of T . We show that if T is superrosy with \"Equation missing\"<!-- image only, no MathML or LaTex -->-rank 1 then $$T_P$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>P</mml:mi> </mml:msub> </mml:math> is superrosy with \"Equation missing\"<!-- image only, no MathML or LaTex -->-rank at most $$omega $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ω</mml:mi> </mml:math> .","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computable approximations of a chainable continuum with a computable endpoint","authors":"Zvonko Iljazović, Matea Jelić","doi":"10.1007/s00153-023-00891-5","DOIUrl":"https://doi.org/10.1007/s00153-023-00891-5","url":null,"abstract":"","PeriodicalId":8350,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135734368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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