## Journal of Symbolic Logic

### Wadge Hierarchy and Veblen Hierarchy Part I: Borel Sets of Finite Rank

J. Duparc

#### Abstract

We consider Borel sets of finite rank $A \subseteq\Lambda^\omega$ where cardinality of $\Lambda$ is less than some uncountable regular cardinal $\mathcal{K}$. We obtain a "normal form" of A, by finding a Borel set $\Omega$, such that A and $\Omega$ continuously reduce to each other. In more technical terms: we define simple Borel operations which are homomorphic to ordinal sum, to multiplication by a countable ordinal, and to ordinal exponentiation of base $\mathcal{K}$, under the map which sends every Borel set A of finite rank to its Wadge degree.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 1 (2001), 56-86.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746360

Mathematical Reviews number (MathSciNet)
MR1825174

Zentralblatt MATH identifier
0979.03039

JSTOR