# On forcing and the (elusive) free two-generated left distributive algebra

## Sheila Miller

### City Tech - CUNY

We begin with an extended introduction to free left distributive algebras (LDs) including a normal form theorem for the one-generated free LD, which itself arises naturally from the assumption of a very large cardinal axiom. After discussing some applications and open problems, we make remarks on the difficulty of using forcing to attempt to construct a two-generated free LD by lifting the rank-to-rank elementary embedding used to create the one-generated free LD.

This is joint work with Joel David Hamkins.

Sheila Miller is an Assistant Professor at the New York City College of Technology, in CUNY. She received her Ph.D. from the University of Colorado at Boulder in 2007, with a thesis entitled “Free Left-Distributive Algebras,” written under the supervision of Richard Laver, and subsequently held a postdoctoral position at the USMA in West Point. In addition to set theory and distributive algebras, she studies mathematical biology, with ongoing research into populations of sea turtles.