{"title":"可数无原子布尔代数的泛函约化","authors":"Bertalan Bodor, Kende Kalina, Csaba A. Szabó","doi":"10.1142/s0218196723500078","DOIUrl":null,"url":null,"abstract":"For an algebra [Formula: see text] the algebra [Formula: see text] is called a functional reduct if each [Formula: see text] is a term function of [Formula: see text]. We classify the functional reducts of the countable atomless Boolean algebra up to first-order interdefinability. That is, we consider two functional reducts the “same” if their group of automorphisms is the same. We show that there are 13 such reducts and describe their structures and group of automorphisms.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":"15 1","pages":"87-103"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Functional reducts of the countable atomless Boolean algebra\",\"authors\":\"Bertalan Bodor, Kende Kalina, Csaba A. Szabó\",\"doi\":\"10.1142/s0218196723500078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an algebra [Formula: see text] the algebra [Formula: see text] is called a functional reduct if each [Formula: see text] is a term function of [Formula: see text]. We classify the functional reducts of the countable atomless Boolean algebra up to first-order interdefinability. That is, we consider two functional reducts the “same” if their group of automorphisms is the same. We show that there are 13 such reducts and describe their structures and group of automorphisms.\",\"PeriodicalId\":13615,\"journal\":{\"name\":\"Int. J. Algebra Comput.\",\"volume\":\"15 1\",\"pages\":\"87-103\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Algebra Comput.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218196723500078\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196723500078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Functional reducts of the countable atomless Boolean algebra
For an algebra [Formula: see text] the algebra [Formula: see text] is called a functional reduct if each [Formula: see text] is a term function of [Formula: see text]. We classify the functional reducts of the countable atomless Boolean algebra up to first-order interdefinability. That is, we consider two functional reducts the “same” if their group of automorphisms is the same. We show that there are 13 such reducts and describe their structures and group of automorphisms.
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