{"title":"树木无限鸽子洞原理的守恒强度","authors":"Chitat Chong, Wei Wang, Yue Yang","doi":"10.1007/s11856-023-2567-8","DOIUrl":null,"url":null,"abstract":"Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 2 2 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 2 2 + WKL0 is Π 3 0 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the same Π 3 0 -sentences.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Conservation strength of the infinite pigeonhole principle for trees\",\"authors\":\"Chitat Chong, Wei Wang, Yue Yang\",\"doi\":\"10.1007/s11856-023-2567-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 2 2 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 2 2 + WKL0 is Π 3 0 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the same Π 3 0 -sentences.\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-023-2567-8\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11856-023-2567-8","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Conservation strength of the infinite pigeonhole principle for trees
Let TT1 be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let RT 2 2 and WKL0 denote respectively the principles of Ramsey’s theorem for pairs and the weak König lemma. It is proved that TT1 + RT 2 2 + WKL0 is Π 3 0 -conservative over the base system RCA0. Thus over RCA0, TT1 and Ramsey’s theorem for pairs prove the same Π 3 0 -sentences.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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