Research

Welcome to my research page! If you have to choose one must-read paper among my list, take this one. I also wrote a list of open questions I would like to see solved. Damir Dzhafarov maintains a reverse mathematics zoo.

Journal papers

  1. P. Cholak, L. Patey. Thin set theorems and cone avoidance
    Transactions of the AMS, to appear.
  2. D. D. Dzhafarov, J. Goh, D. R. Hirschfeldt, L. Patey and A. Pauly
    Ramsey's theorem and products in the Weihrauch degrees
    Computability, to appear.
  3. B. Monin, L. Patey. Pigeons do not jump high
    Advances in Mathematics, to appear.
  4. P. Cholak, G. Igusa, L. Patey, M. Soskova, and D. Turetsky. The Rado path decomposition theorem
    Israel Journal of Mathematics, to appear.
  5. L. Liu, B. Monin, and L. Patey. A computable analysis of variable words theorems
    Proceedings of the AMS, 147 (2019), no. 2, 823--834.
  6. K. Yokoyama, L. Patey. The proof-theoretic strength of Ramsey's theorem for pairs and two colors
    Advances in Mathematics, 330 (2018), 1034--1070.
  7. D. D. Dzhafarov, L. Patey. Coloring trees in reverse mathematics
    Advances in Mathematics, 318 (2017), 497--514.
  8. L. Patey. Partial orders and immunity in reverse mathematics
    Computability, 7 (2018) no. 4, 323--339.
  9. L. Patey. The reverse mathematics of non-decreasing subsequences
    Archive for Mathematical Logic, 56 (2017), no. 5-6, 491--506.
  10. L. Patey. Dominating the Erdos-Moser theorem in reverse mathematics
    Annals of Pure and Applied Logic, 168 (2017), no. 6, 1172--1209.
  11. B. Monin, L. Patey. Pi01 encodability and omniscient reductions
    Notre Dame Journal of Formal Logic, 60 (2019), no. 1, 1--12.
  12. L. Bienvenu, L. Patey, and P. Shafer
    On the logical strengths of partial solutions to mathematical problems
    Transactions of the London Mathematical Society, 4 (2017), no. 1, 30--71.
    Previously named A Ramsey-type König's lemma and its variants
  13. E. Frittaion and L. Patey. Coloring the rationals in reverse mathematics
    Computability, 6 (2017), no. 4, 319--331.
  14. D. D. Dzhafarov, L. Patey, D. R. Solomon and L. B. Westrick.
    Ramsey's theorem for singletons and strong computable reducibility
    Proceedings of the AMS, 145 (2017), no. 3, 1343--1355.
  15. L. Patey. The weakness of being cohesive, thin or free in reverse mathematics
    Israel Journal of Mathematics, 216 (2016), no. 2, 905--955.
    Previously named Dissent within cohesiveness in reverse mathematics
  16. L. Bienvenu and L. Patey. Diagonally non-computable functions and fireworks
    Information and Computation, 253 (2017), part 1, 64--77.
  17. L. Patey. Controlling iterated jumps of solutions to combinatorial problems
    Computability, 6 (2017), no. 1, 47--78.
  18. L. Patey. Open questions about Ramsey-type statements in reverse mathematics
    Bulletin of Symbolic Logic, 22 (2016), no. 2, 151--169.
  19. L. Patey. The strength of the tree theorem for pairs in reverse mathematics
    Journal of Symbolic Logic, 81 (2016), no. 4, 1481--1499.
  20. L. Patey. Iterative forcing and hyperimmunity in reverse mathematics
    Computability, 6 (2017), no. 3, 209--221.
  21. L. Patey. Ramsey-type graph coloring and diagonal non-computability
    Archive for Mathematical Logic 54 (2015), no. 7-8, 899--914
  22. L. Patey. Degrees bounding principles and universal instances in reverse mathematics
    Annals of Pure and Applied Logic 166 (2015), no. 11, 1165--1185.
  23. L. Patey. The complexity of satisfaction problems in reverse mathematics
    Computability, 4(1):69–84, 2015.

Conference papers

  1. L. Patey. Partial orders and immunity in reverse mathematics
    Computability in Europe 2016
  2. L. Patey. Iterative forcing and hyperimmunity in reverse mathematics
    Computability in Europe 2015 (Best student paper award)
  3. L. Patey. The complexity of satisfaction problems in reverse mathematics
    Computability in Europe 2014 (Best student paper award)
  4. G. Bisson, L. Patey. Les «arbres empilés»: une nouvelle approche pour la visualisation des grands dendrogrammes. Actes de la conférence IHM'09, :7, Grenoble, oct 2009.

Submitted

  1. Ramsey-like theorems and moduli of computation (pdf)
  2. Some results concerning the SRT22 vs COH problem
    with P. Cholak, D. D. Dzhafarov, and D. R. Hirschfeldt (pdf)
  3. Relationships between computability-theoretic properties of problems
    with R. Downey, N. Greenberg, M. Harrison-Trainor, and D. Turetsky (pdf)
  4. COH, SRT22, and multiple functionals
    with D. D. Dzhafarov (pdf)
  5. SRT22 does not imply COH in omega-models with B. Monin (pdf)
  6. The weakness of the pigeonhole principle under hyperarithmetical reductions
    with B. Monin (pdf)

Ongoing projects

  1. The role of randomness in reverse mathematics with L. Bienvenu and P. Shafer
  2. Combinatorial weaknesses of Ramseyan principles (draft)
  3. On the strictness of Ramsey-type hierachies in reverse mathematics

Unpublished results

  1. L. Patey. The reverse mathematics of Ramsey-type theorems Ph.D thesis. 2016
  2. L. Patey. Somewhere over the rainbow Ramsey theorem for pairs. Not worthy paper. 2015
  3. L. Patey. A note on "Separating principles below Ramsey's theorem for pairs" 2013
  4. L. Patey. Reverse Mathematics and a Weak Ramsey-Type König’s Lemma. Internship report. 2012
  5. L. Patey. CPS Transformation of Lisp-Like Multi-Staged Languages Extended version. 2011
  6. L. Patey. Eternity II et variantes. Internship report. 2010