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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…
Notes on Interpretability between Weak First-order Theories: Theories of Sequences
Lars Kristiansen, Juvenal Murwanashyaka
We introduce a first-order theory which is mutually interpretable with Robinson's . The universe of a standard model for consists of seque…
There are no minimal essentially undecidable Theories
Fedor Pakhomov, Juvenal Murwanashyaka, Albert Visser
We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.
Weak Essentially Undecidable Theories of Concatenation II
Juvenal Murwanashyaka
We show that we can interpret concatenation theories in arithmetical theories without coding sequences.
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…