3 papers
math.LO2025
Tightness and solidity in fragments of Peano Arithmetic
Piotr Gruza, Leszek Aleksander Kołodziejczyk, Mateusz Łełyk
It was shown by Visser that Peano Arithmetic has the property that any two bi-interpretable extensions of it (in the same language) are equivalent. Enayat proposed to refer to this…
math.LO2025
Definiteness properties of first-order schemes
Piotr Gruza, Mateusz Łełyk
The paper aims to establish a convenient formal framework for investigating the phenomenon of scheme definiteness, exemplified by first-order internal categoricity as studied by Vä…
math.LO2023
Varieties of truth definitions
Piotr Gruza, Mateusz Łełyk
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sent…