Scholarlink

We analyze computable algebras (in the sense of universal algebra) in terms of index set complexity, specifically as regards their congruence lattices. We characterize simplicity of lattices as complete at the level \(\varPi ^0_2\) , mirroring a result of Khoussainov and Morozov (2010) for groups. Finiteness of the congruence lattice is proved complete at the level \(\varSigma ^0_3\) ; and subdirect irreducibility at the level \(\varSigma ^0_3\) .

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Index Set Complexity for Congruence Lattices of Lattices

  • 会议论文

  • 发表日期：

    2026年

查看全文
  • Bjørn Kjos-Hanssen,
  • Paul Kim Long V. Nguyen

摘要

We analyze computable algebras (in the sense of universal algebra) in terms of index set complexity, specifically as regards their congruence lattices. We characterize simplicity of lattices as complete at the level \(\varPi ^0_2\) , mirroring a result of Khoussainov and Morozov (2010) for groups. Finiteness of the congruence lattice is proved complete at the level \(\varSigma ^0_3\) ; and subdirect irreducibility at the level \(\varSigma ^0_3\) .