Elementary properties of free lattices III: Undecidability of the full theory
Abstract
In the work of Nation and Paolini [Sel. Math. New Ser. (32) 41 (2026)] we proved that the universal theory of infinite free lattices is (algorithmically) decidable, leaving open the problem of decidability of the full theory of an (infinite) free lattice. We solve this problem by proving that, for every cardinal κ ≥ 3 \kappa \geq 3 , the first-order theory of the free lattice F κ \mathbf {F}_\kappa is undecidable.
Fields of Study & Subjects
Advanced Algebra and Logic
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4893–4901
- Publication date
- 24 April 2026
- Language
- EN