Generalizations of Laver tables

12/06/2018

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by   Joseph Van Name, et al.

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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 E_λ/≡^γ in the sense that composition and the notion of a critical point make sense for these sorts of algebras.