Publications

Papers:

• Reinhard Kahle, Isabel Oitavem, Paulo Guilherme Santos: Numeral completeness of weak theories of arithmetic. Journal of Logic and Computation 2023. DOI:  https://doi.org/10.1093/logcom/exad075.

• Paulo Guilherme Santos, Wilfried Sieg, and Reinhard Kahle: A new perspective on completeness and finitist consistency. Journal of Logic and Computation 2023. DOI:  https://doi.org/10.1093/logcom/exad021.

• Paulo Guilherme Santos and Reinhard Kahle: Variants of Kreisel's conjecture on a new notion of provability. Bulletin of Symbolic Logic, 27(4), 337–350 (2021). DOI: https://doi.org/10.1017/bsl.2021.68.

• Paulo Guilherme Santos and Reinhard Kahle: k-Provability in PA. Logica Universalis, 15, 477–516 (2021). DOI: http://dx.doi.org/10.1007/s11787-021-00278-1.

• Vítor H. Fernandes and Paulo Guilherme Santos: Endomorphisms of semigroups of order-preserving partial transformations. Semigroup Forum, 99, 333-344 (2019). DOI: https://doi.org/10.1007/s00233-018-9948-z.

• Paulo Guilherme Santos and Reinhard Kahle: Diagonalização, Paradoxos e o Teorema de Löb. Revista Portuguesa de Filosofia, 73,1169-1188 (2017). DOI: https://doi.org/10.17990/RPF/2017_73_3_1169 (see JSTOR).

Book Chapter:

• • Reinhard Kahle, Paulo Guilherme Santos: Paradoxes, Intuitionism, and Proof-Theoretic Semantics, Peter Schroeder-Heister on Proof-Theoretic Semantics, Springer, 2024.

    • DOI: https://doi.org/10.1007/978-3-031-50981-0_12.

    • ISBN: 978-3-031-50980-3 (print), 978-3-031-50981-0 (online).

Book:

• • Paulo Guilherme Santos: Diagonalization in Formal Mathematics, BestMasters, Springer, 2020.

    • DOI: https://doi.org/10.1007/978-3-658-29111-2.

    • ISBN: 978-3-658-29110-5 (print), 978-3-658-29111-2 (online).

PhD Thesis:

• • My advisors were Professor Isabel Oitavem and Professor Reinhard Kahle. You can find my thesis here and here.

    • DOI: http://dx.doi.org/10.15496/publikation-90180.

Master's Degree Thesis:

• • My advisors were Professor Reinhard Kahle and Professor Isabel Oitavem: https://run.unl.pt/bitstream/10362/110484/1/Santos_2019.pdf.

Proceedings:

• • Work presented by Reinhard Kahle (joint work with Paulo Guilherme Santos): Proceedings of Proof-Theoretic Semantics, 2019. DOI: http://dx.doi.org/10.15496/publikation-35319.

Posters:

• Paulo Guilherme Santos and Reinhard Kahle: k-provability in Peano Arithmetic. Ciência 2020.

e-prints:

• • António Malheiro and Paulo Guilherme Santos: A Note on a Unifying Proof of the Undecidability of Several Diagrammatic Properties of Term Rewriting Systems. ArXiv: 1910.09254.