Elementary properties of free lattices III: Undecidability of the full theory
In [6] 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 $κ\geq 3$, the first-order theory of the free lattice $\mathbf{F}_κ$ is undecidable.
Authors
- J. B. Nation (ORCID: https://orcid.org/0000-0001-5959-3304)
- Gianluca Paolini (ORCID: https://orcid.org/0000-0002-8266-362X)
Publication Details
- Journal
- Proceedings of the American Mathematical Society
- Published
- 2026-04-18
- DOI
- https://doi.org/10.1090/proc/17766
- Primary Topic
- Advanced Algebra and Logic
- Type
- article
- Field-Weighted Citation Impact
- 0.00