Computer Science – Formal Languages and Automata Theory
Scientific paper
2010-02-08
Computer Science
Formal Languages and Automata Theory
Scientific paper
An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than $\omega^\omega$. It follows that the algebraic ordinals are exactly those less than $\omega^{\omega^\omega}$.
Bloom Stephen L.
Esik Zoltan
No associations
LandOfFree
Algebraic Linear Orderings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Algebraic Linear Orderings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic Linear Orderings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-308533