Janos Ivanyos (ELTE)
Title: Laver tables
Time: Wednesday, 13.05.2026, 14:00.
Place: ELTE, D3-211.
Abstract:
For each nonnegative integer n, the n-th Laver table is the unique 2^n \times 2^n table whose entry in row p and column q is p * q, where * is a binary operation on \{1,2,\dots,2^n\} satisfying left self-distributivity,
p*(q*r)=(p*q)*(p*r),
and the recursion
p*1 \equiv p+1 \pmod{2^n}.
In this talk, I will show that the I3 axiom implies that the period of the first row of the n-th Laver table tends to infinity as n\to\infty. Here, the I3 axiom asserts the existence of a nontrivial elementary embedding j: V_\lambda \to V_\lambda, where V_\lambda denotes the \lambda-th level of the von Neumann universe.
This provides an application of large cardinal axioms for a finite (countable) combinatorial problem.