**Authors**: Randall Dougherty and Thomas Jech

**Title:** *Finite left-distributive algebras and embedding algebras*

Advances in Math. 130 (1997)

**Abstract:** We consider algebras with one binary operation
one generator and satisfying the left distributive law.
One can define a sequence of finite
left-distributive algebras A_n, and then take a limit to get an infinite
monogenic left-distributive algebra A. Results of Laver and Steel
assuming a strong large cardinal axiom imply that A is free; it is
open whether the freeness of A can be proved without the large
cardinal assumption, or even in Peano arithmetic. The main result of this
paper is the equivalence of this problem with the existence of a certain
algebra of increasing functions on natural numbers, called an *embedding
algebra.* Using this and results of the first author, we conclude that the
freeness of A is unprovable in primitive recursive arithmetic.

**Author**: Thomas Jech

**Title:** *Large ordinals*

Advances in Math. 125 (1997)

**Abstract:** We investigate ordinals associated with cyclic
left-distributive algebras.

**Authors**: Randall Dougherty and Thomas Jech

**Title:** *Left-distributive embedding algebras*

Electr. Res. Ann. AMS 3 (1997)

**Abstract:** This paper is an abridged version (without proofs) of
a forthcoming paper in Advances in Mathematics.