7 citations · 7 across the 7 of their papers we have counts for
7 papers
Entangled Suslin lines and OGA
Carlos Martinez-Ranero, Lucas Polymeris
We construct a model of the Open Graph Axiom (OGA) in which there is a 2-entangled Suslin line . Consequently, in this model, there is a 2-entangled uncountable linear order, bu…
The class of Aronszajn lines under epimorphisms
Lucas Polymeris, Carlos Martinez-Ranero
A linear order is called strongly surjective if for every non empty suborder , there is an epimorphism from onto (denoted by ). We sho…
Undecidability of infinite towers of Kummer extensions of
Carlos Martinez-Ranero, Javier Utreras
We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combine…
Undecidability of infinite algebraic extensions of
Carlos Martinez-Ranero, Dubraska Salcedo, Javier Utreras
Building on work of J. Robinson and A. Shlapentokh, we develop a general framework to obtain definability and decidability results of large classes of infinite algebraic extensions…
Autohomeomorphisms of the finite powers of the double arrow
Sebastian Barria, Carlos Martinez-Ranero
Let and denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that any homeomorphism is l…
Existential decidability for addition and divisibility in holomorphy subrings of global fields
Carlos Martinez-Ranero, Javier Utreras, Xavier Vidaux
We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of glob…
Undecidability of
Carlos Martinez-Ranero, Javier Utreras, Carlos R. Videla
It is shown that the compositum of all degree 2 extensions of has undecidable theory.