Wadge Hierarchy and Veblen Hierarchy Part I: Borel Sets of Finite Rank
Duparc, J.
J. Symbolic Logic, Tome 66 (2001) no. 1, p. 56-86 / Harvested from Project Euclid
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.
Publié le : 2001-03-14
Classification: 
@article{1183746360,
     author = {Duparc, J.},
     title = {Wadge Hierarchy and Veblen Hierarchy Part I: Borel Sets of Finite Rank},
     journal = {J. Symbolic Logic},
     volume = {66},
     number = {1},
     year = {2001},
     pages = { 56-86},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746360}
}
Duparc, J. Wadge Hierarchy and Veblen Hierarchy Part I: Borel Sets of Finite Rank. J. Symbolic Logic, Tome 66 (2001) no. 1, pp.  56-86. http://gdmltest.u-ga.fr/item/1183746360/