Kristina Ago, Bojan Bašić, Milica Maksimović, Milica Šobot
{"title":"On finite models of Hilbert's incidence geometry","authors":"Kristina Ago, Bojan Bašić, Milica Maksimović, Milica Šobot","doi":"10.1016/j.disc.2024.114159","DOIUrl":null,"url":null,"abstract":"<div><p>We consider finite models of the first group of Hilbert's axioms of the Euclidean geometry (the so-called axioms of incidence). We give a lower bound on the number of such models with <em>n</em> points, and we calculate their exact number for <em>n</em> up to 12.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24002905","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider finite models of the first group of Hilbert's axioms of the Euclidean geometry (the so-called axioms of incidence). We give a lower bound on the number of such models with n points, and we calculate their exact number for n up to 12.