English

Bqo is Pi^1_2-complete

Logic 2010-03-26 v1

Abstract

In this paper we prove that the set of countable bqos (viewed as a subset of the Cantor space) is Pi^1_2-complete. The notion of bqo or better quasi-ordering arises from combinatorics and is a generalization of the canonical example of a Pi^1_1-complete notion, i.e. that of countable well-ordering. The Pi^1_2-completeness of bqo was conjectured by Clote and proved by the author in his Ph.d. thesis: in this paper we prove it using Simpson's definition of bqo and as little bqo theory as possible.

Cite

@article{arxiv.math/9405207,
  title  = {Bqo is Pi^1_2-complete},
  author = {Alberto Marcone},
  journal= {arXiv preprint arXiv:math/9405207},
  year   = {2010}
}