4 citations · 10 across the 10 of their papers we have counts for
11 papers · 1 filter
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.
Constructing Wadge classes
Raphaël Carroy, Andrea Medini, Sandra Müller
We show that, assuming the Axiom of Determinacy, every non-selfdual Wadge class can be constructed by starting with those of level (that is, the ones that are closed under Bo…
Minimal definable graphs of definable chromatic number at least three
Raphael Carroy, Benjamin D. Miller, David Schrittesser +1
We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of…
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…
Embeddability on functions: order and chaos
Raphaël Carroy, Yann Pequignot, Zoltán Vidnyánszky
We study the quasi-order of topological embeddability on definable functions between Polish zero-dimensional spaces. We first study the descriptive complexity of this quasi-order r…
Linear orders: when embeddability and epimorphism agree
Riccardo Camerlo, Raphaël Carroy, Alberto Marcone
When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective line…