{"title":"Ordinal Numbers and the Transfinite","authors":"","doi":"10.1142/9789811201936_0005","DOIUrl":"https://doi.org/10.1142/9789811201936_0005","url":null,"abstract":"","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130129194","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":"Real Numbers","authors":"","doi":"10.1142/9789811201936_0007","DOIUrl":"https://doi.org/10.1142/9789811201936_0007","url":null,"abstract":"","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"52 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123708606","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":"Natural Numbers and Countable Sets","authors":"","doi":"10.1142/9789811201936_0004","DOIUrl":"https://doi.org/10.1142/9789811201936_0004","url":null,"abstract":"","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121209733","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":"FRONT MATTER","authors":"","doi":"10.1142/9789811201936_fmatter","DOIUrl":"https://doi.org/10.1142/9789811201936_fmatter","url":null,"abstract":"","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121842669","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":"Ramsey Theory","authors":"Justen Holl, Elizabeth Tso, Julia Balla, Fall","doi":"10.1142/9789811201936_0009","DOIUrl":"https://doi.org/10.1142/9789811201936_0009","url":null,"abstract":"Ramsey Theory is the study of how specific patterns inevitably emerge in sufficiently large systems. This paper provides an overview of three key theorems in Ramsey Theory: Ramsey’s Theorem, Van der Waerden’s Theorem, and Rado’s Theorem, which deal with finding patterns in mathematical objects such as graphs, the number line, and systems of linear equations respectively. While each theorem is distinctly different, they share a common objective of discerning order in chaos.","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123519486","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":"Review of Sets and Logic","authors":"","doi":"10.1142/9789811201936_0002","DOIUrl":"https://doi.org/10.1142/9789811201936_0002","url":null,"abstract":"","PeriodicalId":114605,"journal":{"name":"Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127327807","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}