Back to Search
Start Over
Algebraic Linear Orderings
- Publication Year :
- 2010
- Publisher :
- arXiv, 2010.
-
Abstract
- 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 ωω. It follows that the algebraic ordinals are exactly those less than ωωω.
- Subjects :
- Discrete mathematics
FOS: Computer and information sciences
Function field of an algebraic variety
Formal Languages and Automata Theory (cs.FL)
Algebraic extension
Computer Science - Formal Languages and Automata Theory
Dimension of an algebraic variety
Algebraic closure
Algebraic cycle
Algebraic surface
Computer Science (miscellaneous)
Real algebraic geometry
Differential algebraic geometry
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2ed7bc7941669768144828f0957edff3
- Full Text :
- https://doi.org/10.48550/arxiv.1002.1624