3 papers
math.LO2025
Elementary properties of free lattices III: Undecidability of the full theory
J. B. Nation, Gianluca Paolini
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) fr…
math.LO2025
Elementary properties of free lattices II: Decidability of the universal theory
J. B. Nation, Gianluca Paolini
We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existen…
math.LO2023
Elementary Properties of Free Lattices
J. B. Nation, Gianluca Paolini
We start a systematic analysis of the first-order model theory of free lattices. Firstly, we prove that the free lattices of finite rank are not positively indistinguishable, as th…