7 papers
No Countable Basis for Borel Directed Graphs of Dichromatic Number at Least Three
Tonatiuh Matos-Wiederhold
I prove that the Borel directed graphs whose vertex set admits a partition into two Borel acyclic sets form a -complete set; equivalently, that deciding whether a Bor…
A Concise Proof of the Dichotomy
Tonatiuh Matos-Wiederhold
Carroy, Miller, Schrittesser, and Vidnyánszky established the dichotomy: there is a Borel graph of Borel chromatic number three that admits a continuous homomorphism to every…
Complexity of deep computations via topology of function spaces
Eduardo Dueñez, José Iovino, Tonatiuh Matos-Wiederhold +2
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta,…
Uncountable sets and an infinite linear order game
Tonatiuh Matos-Wiederhold, Luciano Salvetti
An infinite game on the set of real numbers appeared in Matthew Baker's work [Math. Mag. 80 (2007), no. 5, pp. 377--380] in which he asks whether it can help characterize countable…
New recursive constructions of amoebas and their balancing number
Laura Eslava, Adriana Hansberg, Tonatiuh Matos Wiederhold +1
The definition of amoeba graphs is based on iterative \emph{feasible edge-replacements}, where, at each step, an edge from the graph is removed and placed in an available spot in a…
The Open Coloring Axiom
Tonatiuh Matos-Wiederhold
This work is concerned with an axiom introduced by Todorcěvić in \cite{stevo} that constitutes a Ramsey-like statement regarding the topology of the reals. Our aim is to explain th…