Marcel Jackson

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math.LO2026

Multiplicatively idempotent HSI algebras satisfy all equations of $N$

Tumadhir Alsulami, Marcel Jackson, Michael Kinyon

An algebra with binary operations $+, \cdot, ↑$ and constant $1$ is called an HSI algebra if it satisfies the basic commutative semiring laws for $+, \cdot, 1$ on~ $N$ a…

math.LO2024

Finite models for positive combinatorial and exponential algebra

Tumadhir Alsulami, Marcel Jackson

We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory h…

Multiplicatively idempotent HSI algebras satisfy all equations of N

Finite models for positive combinatorial and exponential algebra

Multiplicatively idempotent HSI algebras satisfy all equations of $N$