{"title":"Profiniteness, monadicity and universal models in modal logic","authors":"Matteo De Berardinis, Silvio Ghilardi","doi":"10.1016/j.apal.2024.103454","DOIUrl":null,"url":null,"abstract":"<div><p>Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over <strong>Set</strong>. While analyzing the monadic functor, we recover the universal model construction - a construction widely used in the modal logic literature for describing finitely generated free modal algebras and the essentially finite generated subframes of their canonical models.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 7","pages":"Article 103454"},"PeriodicalIF":0.6000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007224000526","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
Abstract
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction widely used in the modal logic literature for describing finitely generated free modal algebras and the essentially finite generated subframes of their canonical models.
期刊介绍：
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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