3 papers
math.LO2025
The barrier Ramsey theorem
Alberto Marcone, Antonio Montalbán, Andrea Volpi
In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set t…
math.LO2022
The -Vaught's Conjecture
David Gonzalez, Antonio Montalbán
We introduce the -Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a struct…
math.LO2022
The structural complexity of models of arithmetic
Antonio Montalbán, Dino Rossegger
We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than and that non-standard models of…