35 citations · 52 across the 14 of their papers we have counts for
4 papers · 1 filter
Descending sequences in reflection hierarchies
Mateusz Łełyk, James Walsh
There is no recursively enumerable sequence of sufficiently strong 2-consistent r.e. theories such that each proves the -consistency of the next. Montalbán and Shavrukov indepen…
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…
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…
Classifying the complexity of models of arithmetic
David Gonzalez, Mateusz Łełyk, Dino Rossegger +1
We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored line…