无穷代数上量词的自由可定义性

2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2016-07-05 DOI:10.1145/2933575.2934572

B. Khoussainov

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引用次数: 1

摘要

在代数A的定义域A上，如果存在一个一阶逻辑公式φ (x ā， y)，且参数来自A，使得对于所有∈An和b∈A, f(ā)=b iff (ā，b)，则运算f: An→A是可定义的。本文的目的是从可计算性和模型论可定义性的角度研究可数无穷代数上无量子公式运算的可定义性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Quantifier Free Definability on Infinite Algebras

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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来源期刊

2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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