# Generalized Laver tables II

## Joseph Van Name

### CUNY Borough of Manhattan Community College

We shall investigate several classes of left-distributive algebras that behave like algebras of elementary embeddings including permutative LD-systems, locally Laver-like LD-systems, and generalized Laver tables. In these algebras, there is a notion of a critical point, a composition operation, and the notion of equivalence up to a certain critical point. Furthermore, the locally Laver-like LD-systems are used to generate and classify generalized Laver tables. After discussing the general theory of these algebras, we shall show that there exists generalized Laver tables which cannot arise from algebras of elementary embeddings. We shall then give a framework that allows us to construct from rank-into-rank embeddings finite algebras that satisfy the distributivity identity $x*f(x_{1},…,x_{n})=f(x*x_{1},…,x*x_{n})$ where $(X,*)$ is a left-distributive algebra.

Joseph Van Name received his PhD from the University of South Florida in 2013. He is interested in Boolean algebras, ordered sets, general topology, point-free topology, set-theory, universal algebra, and model theory. Most of his mathematics research involves dualities that are similar to Stone duality.