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Papers on weak first-order theories and decidability problems

Part of: Discrete mathematics in relation to computer science General logic Proof theory and constructive mathematics Computability and recursion theory

Published online by Cambridge University Press:  15 December 2025

Juvenal Murwanashyaka
Juvenal Murwanashyaka*
Affiliation:
University of Oslo. 2023.
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Abstract

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The dissertation consists of an introductory chapter and eight published articles centered around the following topics: (1) calibration of the interpretability strength of weak first-order theories; (2) determination of the (un)decidability of fine-grained fragments of the intended models of the aforementioned theories; and (3) investigation of algebraic properties of the lattice of interpretability degrees of computably enumerable essentially undecidable theories.

  1. 1. J. Murwanashyaka, A weak theory of building blocks. Mathematical Logic Quarterly, vol. 70 (2024), pp. 233–254. doi: 10.1002/malq.202300015

  2. 2. J. Murwanashyaka, Hilbert’s tenth problem for term algebras with a substitution operator. Computability, vol. 13 (2024), nos. 3–4, pp. 433–457. doi: 10.3233/COM-230444

  3. 3. J. Murwanashyaka, Weak essentially undecidable theories of concatenation, part II. Archive for Mathematical Logic, vol. 63 (2024), pp. 353–390. doi: 10.1007/s00153-023-00898-y

  4. 4. J. Murwanashyaka, F. Pakhomov, and A. Visser, There are no minimal essentially undecidable theories. Journal of Logic and Computation, vol. 34 (2024), no. 6, pp. 1159–1171. doi: 10.1093/logcom/exad005

  5. 5. J. Murwanashyaka, Weak essentially undecidable theories of concatenation. Archive for Mathematical Logic, vol. 61 (2022), nos. 7–8, pp. 939–976. doi: 10.1007/s00153-022-00820-y.

  6. 6. J. Murwanashyaka, Weak sequential theories of finite full binary trees, Revolutions and Revelations in Computability (U. Berger, J. N. Y. Franklin, F. Manea, and A. Pauly, editors), CiE 2022, Lecture Notes in Computer Science, Vol. 13359, Springer International Publishing, 2022, pp. 208–219. doi: 10.1007/978-3-031-08740-0_18.

  7. 7. L. Kristiansen and J. Murwanashyaka, First-order concatenation theory with bounded quantifiers. Archive for Mathematical Logic, vol. 60 (2021), nos. 1–2, pp. 77–104. doi: 10.1007/s00153-020-00735-6.

  8. 8. L. Kristiansen and J. Murwanashyaka, On interpretability between some weak essentially undecidable theories, Beyond the Horizon of Computability (M. Anselmo, G. Della Vedova, F. Manea, and A. Pauly, editors), CiE 2020, Lecture Notes in Computer Science, Vol. 12098, Springer International Publishing, 2020, pp. 63–74. doi: 10.1007/978-3-030-51466-2_6.

Abstract prepared by Juvenal Murwanashyaka

E-mail: murwanashyaka@math.cas.cz

URL: http://hdl.handle.net/10852/104677

Keywords

decidabilityinterpretabilitysequential theoriesweak arithmetic

MSC classification

Primary: 03B10: Classical first-order logic 03B25: Decidability of theories and sets of sentences 03D35: Undecidability and degrees of sets of sentences 03D40: Word problems, etc. 03F25: Relative consistency and interpretations 03F30: First-order arithmetic and fragments 68R15: Combinatorics on words

Information

Type
Thesis Abstract
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 4 , December 2025 , pp. 696
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Footnotes

Supervised by Lars Kristiansen, Dag Normann, and Tom Lindstrøm