Carlos Martinez Ranero, Universidad de Concepción

# Carlos Martínez Ranero, Universidad de Concepción

E-mail:
cmartinezr (at) udec (dot) cl

I am an associate professor at the Department of Mathematics, University of Concepción, Chile.
I am currently the Director of our Master's Program in Mathematics.

Research: I'm interested in mathematical logic, broadly speaking, particularly set theory. I currently work with cardinal characteristics of the continuum, Aronszajn trees, and I have also explored connections with number theory through Hilbert's Tenth Problem.

I completed my PhD at University of Toronto in 2010 under Stevo Todorcevic. From 2011-2013 I was a postdoctoral fellow at UNAM, campus Morelia. From 2013-2017 I was an assistant professor at University of Concepcion.

## Publications and preprints

1. Autohomeomorphisms of the finite powers of the double arrow, (with Sebastián Barría)
arXiv:2208.00509
2. Existential decidability for addition and divisibility in holomorphy subrings of global fields, (with Javier Utreras, Xavier Vidaux)
Journal of Number Theory 241 (2022), 504-530.
arXiv:2010.14024
3. Hereditary Intervals Algebras and Cardinal Characteristics of the Continuum, (with M. Hrušák, A. Ramos-García)
Israel J. Math. 242 (2) 2021, no. 2, 769-795.
arXiv:1905.13398
4. The diophantine problem for addition and divisibility for subrings of rational functions over finite fields. (with L. Cerda-Romero)
Proyecciones, vol 39, no. 3 (2020), 721--735. Link to paper
5. Undecidability of $$\mathbb Q^{(2)}$$, (with J. Utreras, C. Videla)
Proc. Amer. Math. Soc. 148 (2020), 961-964
arXiv:1809.04670
6. On a construction of Malykhin. (with A. Ramos-García)
Topology Proceedings 53 (2019), 209--218. Link to paper
7. The Diophantine problem for addition and divisibility over subrings of the rationals. (with L. Cerda-Romero)
J. of Symb. Logic 82 (2017), no. 3, 1140--1149. Link to paper
8. Generic existence of MAD families. (with O. Guzmán-González, M. Hrušák, A. Ramos-García)
J. of Symb. Logic 82 (2017), no. 1, 303--316. Link to paper