{"title":"Quantifier Free Definability on Infinite Algebras","authors":"B. Khoussainov","doi":"10.1145/2933575.2934572","DOIUrl":null,"url":null,"abstract":"An operation f : A<sup>n</sup> → A on the domain A of an algebra A is definable if there exists a first order logic formula ϕ ( x̄ , y ) with parameters from A such that for all ā ∈ A<sup>n</sup> and b ∈ A we have f(ā)=b iff 𝒜 | = ϕ(ā,b). The goal of this paper is to study definability of operations by quantifier-free formulas on countable infinite algebras from computability and model-theoretic definability points of view.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2933575.2934572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
An operation f : An → A on the domain A of an algebra A is definable if there exists a first order logic formula ϕ ( x̄ , y ) with parameters from A such that for all ā ∈ An and b ∈ A we have f(ā)=b iff 𝒜 | = ϕ(ā,b). The goal of this paper is to study definability of operations by quantifier-free formulas on countable infinite algebras from computability and model-theoretic definability points of view.
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