{"title":"On collection schemes and Gaifman's splitting theorem","authors":"Taishi Kurahashi, Yoshiaki Minami","doi":"10.1002/malq.202400021","DOIUrl":null,"url":null,"abstract":"<p>We study model theoretic characterizations of various collection schemes over <span></span><math>\n <semantics>\n <msup>\n <mi>PA</mi>\n <mo>−</mo>\n </msup>\n <annotation>$\\mathsf {PA}^-$</annotation>\n </semantics></math> from the viewpoint of Gaifman's splitting theorem. Among other things, we prove that for any <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>≥</mo>\n <mn>0</mn>\n </mrow>\n <annotation>$n \\ge 0$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mrow>\n <mi>M</mi>\n <mo>⊧</mo>\n <msup>\n <mi>PA</mi>\n <mo>−</mo>\n </msup>\n </mrow>\n <annotation>$M \\models \\mathsf {PA}^-$</annotation>\n </semantics></math>, the following are equivalent: \n\n </p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"70 4","pages":"398-413"},"PeriodicalIF":0.4000,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Logic Quarterly","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202400021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
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Abstract
We study model theoretic characterizations of various collection schemes over from the viewpoint of Gaifman's splitting theorem. Among other things, we prove that for any and , the following are equivalent:
期刊介绍：
Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.
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