The FC-rank of a context-free language

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than $\omega^\omega$

Laver and set theory

In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip

The Rank of Tree-Automatic Linear Orderings

We generalise Delhomm\'e's result that each tree-automatic ordinal is strictly below \omega^\omega^\omega{} by showing that any tree-automatic linear ordering has FC-rank strictly below \omega^\omega. We further investigate a restricted form of tree-automaticity and prove that every linear ordering which admits a tree-automatic presentation of branching complexity at most k has FC-rank strictly below \omega^k.Comment: 20 pages, 3 figure