4 papers · 1 filter
Bases for functions beyond the first Baire class
Raphaël Carroy, Benjamin D. Miller
We provide a finite basis for the class of Borel functions that are not in the first Baire class, as well as the class of Borel functions that are not -continuous with closed wi…
Sigma-continuity with closed witnesses
Raphaël Carroy, Benjamin D. Miller
We use variants of the dichotomy to establish a refinement of Solecki's basis theorem for the family of Baire-class one functions which are not -continuous with c…
On the existence of small antichains for definable quasi-orders
Raphaël Carroy, Benjamin D. Miller, Zoltán Vidnyánszky
We generalize Kada's definable strengthening of Dilworth's characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.
The open dihypergraph dichotomy and the second level of the Borel hierarchy
Raphaël Carroy, Benjamin D. Miller, Dániel T. Soukup
We show that several dichotomy theorems concerning the second level of the Borel hierarchy are special cases of the -dimensional generalization of the open graph dichotom…