Abstracts: left-distributive algebras

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.