4 citations · 10 across the 10 of their papers we have counts for
13 papers
Some questions on entangled linear orders
Raphaël Carroy, Maxwell Levine, Lorenzo Notaro
Entangled linear orders were first introduced by Abraham and Shelah. Todorčević showed that these linear orders exist under . We prove the following results: (1) If $\…
A well-quasi-order for continuous functions
Raphaël Carroy, Yann Pequignot
We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achie…
A classification of the Wadge hierarchies on zero-dimensional Polish spaces
Raphaël Carroy, Luca Motto Ros, Salvatore Scamperti
We provide a complete classification, up to order-isomorphism, of all possible Wadge hierarchies on zero-dimensional Polish spaces using (essentially) countable ordinals as complet…
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.