English

Algebraic Ordinals

Formal Languages and Automata Theory 2010-02-08 v3 Logic in Computer Science

Abstract

An algebraic tree T is one determined by a finite system of fixed point equations. The frontier \Fr(T) of an algebraic tree t is linearly ordered by the lexicographic order \lex. When (\Fr(T),\lex) is well-ordered, its order type is an \textbf{algebraic ordinal}. We prove that the algebraic ordinals are exactly the ordinals less than ωωω\omega^{\omega^\omega}.

Cite

@article{arxiv.0907.0877,
  title  = {Algebraic Ordinals},
  author = {S. L. Bloom and Z. Esik},
  journal= {arXiv preprint arXiv:0907.0877},
  year   = {2010}
}

Comments

30 pages

R2 v1 2026-06-21T13:21:43.690Z