3 papers
math.LO2022
Essay on modality across different logics
Alfredo Roque Freire, Manuel A. Martins
In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence , we argue that it is not…
math.LO2020
Bi-interpretation in weak set theories
Alfredo Roque Freire, Joel David Hamkins
In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct theories extending ZF are never bi-interpre…
math.LO2019
Does set theory really ground arithmetic truth?
Alfredo Roque Freire
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic…