Jaime Gaspar's homepage

Contacts

• moc.rapsagemiaj@liam
  (PGP key, transition, fingerprint AF33 6D03 5CC3 58E4 99C1 C19E 9822 2D84 6A7F 8BA2)
• www.jaimegaspar.com

Interests

• Provable security and proof presentation in cryptography
• Proof interpretations in mathematical logic

Affiliations

• Algebra and Logic Research Group, Nova Math, Nova School of Science and Technology, Nova University Lisbon, Portugal

Works

• Review of Henry Towsner's article “A worked example of the functional interpretation”
  Review, Mathematical Reviews, MR4900337, May 2026
• Factorisation of the classical nonstandard bounded functional interpretation
  With Bruno Dinis, proceedings of the 2024 Second International Workshop on Mathematics and Physical Sciences; Advances in Mathematical Modeling in Science, Engineering, and Social Sciences, unumbered, pages 71–98, May 2026
• Hardwiring truth in functional interpretations
  With Bruno Dinis, Portugaliae Mathematica, volume 80, numbers 1–2, pages 81–105, February 2023
  PS PDF Permission
• Review of Benno van den Berg's article “A Kuroda-style j-translation”
  Review, Zentralblatt MATH, Zbl 1450.03003, November 2020
  HTML
• Review of Jooyoung Lee's article “Key alternating ciphers based on involutions”
  Review, Mathematical Reviews, MR3779037, November 2019
• Transformation of cryptographic primitives: provable security and proof presentation
  Doctoral dissertation, University of Kent, United Kingdom, November 2019
  PS PDF
• Gödel's first incompleteness theorem (in Portuguese)
  Matemática Universitária, number 54, pages 6–10, September 2018
  PS PDF Permission
• Proof without words: using trapezoids to compute triangular numbers
  Mathematics Magazine, volume 91, number 3, pages 206–207, June 2018
• Intuitionistic nonstandard bounded modified realisability and functional interpretation
  With Bruno Dinis, Annals of Pure and Applied Logic, volume 169, issue 5, pages 392–412, May 2018
• Review of Luís Cruz-Filipe and Fernando Ferreira's article “The finitistic consistency of Heck's predicative Fregean system”
  Review, Zentralblatt MATH, Zbl 1356.03101, February 2017
  HTML
• Mathematical candies
  Proceedings of the 2014 National Meeting of the Portuguese Mathematical Society, Boletim da Sociedade Portuguesa de Matemática, special issue, pages 41–44, May 2016
  PS PDF Permission
• Direct proof of the uncountability of the transcendental numbers (in Chinese)
  Chinese translation of the original English article, 数学译林, issue 4, page 380, 2016
• All triangles at once
  With Orlando Neto, The American Mathematical Monthly, volume 122, number 10, page 982, December 2015
  PS PDF Permission
• Review of Fernando Ferreira and Gilda Ferreira's article “Interpretability in Robinson's Q”
  Review, Zentralblatt MATH, Zbl 1325.03072, September 2015
  HTML
• Review of Gilda Ferreira and Paulo Oliva's article “On the relation between various negative translations”
  Review, Zentralblatt MATH, Zbl 1320.03087, July 2015
  HTML
• Nonstandardness and the bounded functional interpretation
  With Fernando Ferreira, Annals of Pure and Applied Logic, volume 166, issue 6, pages 701–712, June 2015
  PS PDF Permission
• Review of Albert Visser's article “Interpretability degrees of finitely axiomatized sequential theories”
  Review, Zentralblatt MATH, Zbl 1301.03061, November 2014
  HTML
• Copies of classical logic in intuitionistic logic
  14th Congress of Logic, Methodology and Philosophy of Science 2011 Proceedings; Philosophia Scientiae, volume 18, number 3, pages 5–11, November 2014
  PS PDF
• Short introduction by example to Coq and formalising ZF ⊆ ZF_ε in Coq
  Abstract, proceedings of the 2014 3rd International Workshop on Theorem Proving Components for Educational Software, Central Europe Workshop Proceedings, volume 1186, July 2014
  PDF
• “Refuting” Cantor
  Abstract, report on the Logic Colloquium 2013, The Bulletin of Symbolic Logic, volume 20, number 2, June 2014, pages 229–230
  PS PDF
• Does not suffice to run latex a finite number of times to get cross-references right
  Letter, TUGboat, volume 35, number 1, page 16, April 2014
  PS PDF
• Non-recursive polynomial formula for the sum of the powers of the integers
  The American Mathematical Monthly, volume 121, number 2, page 144, February 2014
  HTML
• Direct proof of the uncountability of the transcendental numbers
  The American Mathematical Monthly, volume 121, number 1, page 80, January 2014
  HTML
• Review of Albert Visser's article “Vaught's theorem on axiomatizability by a scheme”
  Review, Zentralblatt MATH, Zbl 1272.03063, August 2013
  HTML
• A theorem with constructive and nonconstructive proofs
  The American Mathematical Monthly, volume 120, number 6, page 536, June 2013
  HTML
• Review of Sy-David Friedman, Michael Rathjen and Andreas Weiermann's article “Slow consistency”
  Review, Zentralblatt MATH, Zbl 1263.03055, May 2013
  HTML
• Negative translations not intuitionistically equivalent to the usual ones
  Studia Logica, volume 101, issue 1, pages 45–63, February 2013
  PS PDF
• Review of Gilda Ferreira and Paulo Oliva's article “On bounded functional interpretations”
  Review, Zentralblatt MATH, Zbl 1251.03074, November 2012
  HTML
• Infinite pigeonhole principle
  Abstract, report on the workshop Mathematical Logic: Proof Theory, Constructive Mathematics 2011; Oberwolfach Reports, volume 8, issue 4, pages 2975–2976, July 2012
• Proof interpretations: theoretical and practical aspects
  Doctoral dissertation, Technical University of Darmstadt, Germany, December 2011
  PS PDF
• Proof interpretations with truth
  Abstract, report on the Logic Colloquium 2010, The Bulletin of Symbolic Logic, volume 17, number 2, pages 296–297, June 2011
  PS PDF Permission
• Proof interpretations with truth
  With Paulo Oliva, Mathematical Logic Quarterly, volume 56, number 6, pages 591–610, December 2010
  PS PDF Permission
• On Tao's “finitary” infinite pigeonhole principle
  With Ulrich Kohlenbach, The Journal of Symbolic Logic, volume 75, number 1, pages 355–371, March 2010
  PS PDF Permission
• Factorization of the Shoenfield-like bounded functional interpretation
  Notre Dame Journal of Formal Logic, volume 50, number 1, pages 53–60, January 2009
  PS PDF HTML Permission
• Around the functional interpretations of arithmetic (in Portuguese)
  Master's thesis, University of Lisbon, Portugal, December 2007
  PS PDF

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