5 papers
Tightness and solidity in fragments of Peano Arithmetic
Piotr Gruza, Leszek Aleksander KoÅodziejczyk, Mateusz ÅeÅyk
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…
Corrigendum & Addendum to "Categoricity-like Properties in the First Order Realm"
Ali Enayat, Mateusz ÅeÅyk
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Descending sequences in reflection hierarchies
Mateusz ÅeÅyk, 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 indepe…
Definiteness properties of first-order schemes
Piotr Gruza, Mateusz ÅeÅyk
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 VÃ…
Classifying the complexity of models of arithmetic
David Gonzalez, Mateusz ÅeÅyk, 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…