5 papers
A non-sequential arithmetical theory with pairing
Juvenal Murwanashyaka
Albert Visser has shown that Robinson's and Gregorczyk's are not sequential by showing that these theories are not even poly-pair theories, which, in…
Friedman's is not parameter-free sequential
Juvenal Murwanashyaka
Harvey Friedman's is a weak set theory given by the following non-logical axioms: $ \mathsf{(W)} \; \forall x y \, \exists z \, \forall u \left[ \, u \in z \leftrig…
Undecidability in First-Order Theories of Term Algebras Extended with a Substitution Operator
Juvenal Murwanashyaka
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Prob…
First-Order Concatenation Theory with Bounded Quantifiers
Lars Kristiansen, Juvenal Murwanashyaka
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a…
Notes on Fragments of First-Order Concatenation Theory
Lars Kristiansen, Juvenal Murwanashyaka
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments…