Generalizations of Laver tables
This work is incremental, extending theoretical structures in set theory and algebra for specialized researchers.
The paper generalizes Laver tables to algebras with multiple generators, various operations, and relaxed self-distributivity, mimicking properties of rank-into-rank embedding algebras such as composition and critical points.
We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are self-distributive or where the operations satisfy a generalized version of self-distributivity. These algebras mimic the algebras of rank-into-rank embeddings $\mathcal{E}_λ/\equiv^γ$ in the sense that composition and the notion of a critical point make sense for these sorts of algebras.