Michael D. Walton

collaborators

3 papers

math.CO2026

The $Z$ -Divisor Graph on $Q \cap [1, 7]$ is Planar and 3-Colorable

Michael D. Walton, Zachary D. Walton

We prove that a divisor graph on an interval of integers is a planar graph whenever the interval $[n, m]$ satisfies $m \leq 7 n$ , and that 7 is the greatest such real number for which…

math.LO2026

Examples of non-tame abstract elementary classes of abelian groups

Daniel Herden, Marcos Mazari-Armida, Michael D. Walton

We construct an abstract elementary class $K_{1}$ of torsion-free abelian groups such that $K_{1}$ is not $(< ℵ_{0})$ -tame but is $ℵ_{0}$ -tame. This answers a question of [BoVa17]…

math.LO2026

An unstable abstract elementary class of modules: A variation of Paolini-Shelah's example

Daniel Herden, Marcos Mazari-Armida, Michael D. Walton

We construct a class $K^$ of torsion-free abelian groups such that $K^= (K^, \leq_{p})$ is an abstract elementary class with $\operatorname{LS}(\hat{\mathbf{K}…

The Z-Divisor Graph on Q∩[1,7] is Planar and 3-Colorable

Examples of non-tame abstract elementary classes of abelian groups

An unstable abstract elementary class of modules: A variation of Paolini-Shelah's example

The $Z$ -Divisor Graph on $Q \cap [1, 7]$ is Planar and 3-Colorable