Research

Welcome to my research page!

Books

  1. B. Monin and L. Patey. Calculabilité : Aléatoire, Mathématiques à rebours et Hypercalculabilité
    Calvage & Mounet, (2022) ISBN 978-2-916352-96-1
  2. L. Levy Patey. Lowness and avoidance In preparation.

Journal papers

  1. L. Levy Patey and A. Mimouni. The weakness of the Erdos-Moser theorem under arithmetic reductions
    Journal of Mathematical Logic, to appear.
  2. Q. Le Houérou, L. Levy Patey and K. Yokoyama. Conservation of Ramsey's theorem for pairs and well-foundedness
    Transactions of the AMS, to appear.
  3. Q. Le Houérou and L. Levy Patey. Pi04 conservation of the Ordered Variable Word theorem
    Journal of Symbolic Logic, to appear.
  4. T. Bompard, L. Liu and L. Levy Patey. The reverse mathematics of Carlson's theorem for located words
    Journal of Combinatorics, to appear.
  5. J. Cervelle, W. Gaudelier and L. Patey. The reverse mathematics of CAC for trees
    Journal of Symbolic Logic, 89 (2024), no.3, pp. 1189--1211.
  6. P.-E. Anglès d’Auriac, B. Mignoty, L. Liu and L. Patey. Carlson-Simpson's lemma and applications in reverse mathematics
    Annals of Pure and Applied Logic, 174 (2023), no.9, pp. 103287.
  7. B. Monin and L. Patey. Partition genericity and pigeonhole basis theorems
    Journal of Symbolic Logic, 89 (2024), no.2, pp. 829 - 857.
  8. L. Liu and L. Patey. The reverse mathematics of the Thin Set and Erdos-Moser theorems
    Journal of Symbolic Logic, 87 (2022), no.1, pp. 313--346.
  9. B. Monin and L. Patey. SRT22 does not imply RT22 in omega-models
    Advances in Mathematics, 389 (2021), pp. 107903, 32.
  10. P.-E. Anglès d'Auriac, P. Cholak, D. D. Dzhafarov, B. Monin and L. Patey.
    Milliken's tree theorem and its applications: a computability-theoretic perspective
    Memoirs of the AMS, 293 (2024), no.1457, pp. vi+118.
  11. N. Greenberg, M. Harrison-Trainor, L. Patey and D. Turetsky.
    Computing sets from all infinite subsets
    Transactions of the AMS, 374 (2021), no.11, pp. 8131--8160.
  12. L. Patey. Ramsey-like theorems and moduli of computation
    Journal of Symbolic Logic , 87 (2022), no.1, pp. 72--108.
  13. R. Downey, N. Greenberg, M. Harrison-Trainor, L. Patey and D. Turetsky
    Relationships between computability-theoretic properties of problems
    Journal of Symbolic Logic , 87 (2022), no.1, pp. 47--71.
  14. B. Monin, L. Patey. The weakness of the pigeonhole principle under hyperarithmetical reductions
    Journal of Mathematical Logic, 21 (2021), no.3, pp. 2150013, 41.
  15. D. D. Dzhafarov and L. Patey. COH, SRT22, and multiple functionals
    Computability, 10 (2021), no. 2, pp. 111--121.
  16. P. Cholak, D. D. Dzhafarov, D. R. Hirschfeldt and L. Patey
    Some results concerning the SRT22 vs COH problem
    Computability, 9 (2020), no. 3-4, pp. 193--217.
  17. P. Cholak, L. Patey. Thin set theorems and cone avoidance
    Transactions of the AMS, 373 (2020), no. 4, 2743--2773.
  18. D. D. Dzhafarov, J. Goh, D. R. Hirschfeldt, L. Patey and A. Pauly
    Ramsey's theorem and products in the Weihrauch degrees
    Computability, 9 (2020), no. 2, 85--110.
  19. B. Monin, L. Patey. Pigeons do not jump high
    Advances in Mathematics, 352, (2019), 1066--1095.
  20. P. Cholak, G. Igusa, L. Patey, M. Soskova, and D. Turetsky.
    The Rado path decomposition theorem
    Israel Journal of Mathematics, Israel J. Math. 234 (2019), no. 1, 179--208.
  21. L. Liu, B. Monin, and L. Patey. A computable analysis of variable words theorems
    Proceedings of the AMS, 147 (2019), no. 2, 823--834.
  22. K. Yokoyama, L. Patey. The proof-theoretic strength of Ramsey's theorem for pairs and two colors
    Advances in Mathematics, 330 (2018), 1034--1070.
  23. D. D. Dzhafarov, L. Patey. Coloring trees in reverse mathematics
    Advances in Mathematics, 318 (2017), 497--514.
  24. L. Patey. Partial orders and immunity in reverse mathematics
    Computability, 7 (2018) no. 4, 323--339.
  25. L. Patey. The reverse mathematics of non-decreasing subsequences
    Archive for Mathematical Logic, 56 (2017), no. 5-6, 491--506.
  26. L. Patey. Dominating the Erdos-Moser theorem in reverse mathematics
    Annals of Pure and Applied Logic, 168 (2017), no. 6, 1172--1209.
  27. B. Monin, L. Patey. Pi01 encodability and omniscient reductions
    Notre Dame Journal of Formal Logic, 60 (2019), no. 1, 1--12.
  28. 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
  29. E. Frittaion and L. Patey. Coloring the rationals in reverse mathematics
    Computability, 6 (2017), no. 4, 319--331.
  30. 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.
  31. 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
  32. L. Bienvenu and L. Patey. Diagonally non-computable functions and fireworks
    Information and Computation, 253 (2017), part 1, 64--77.
  33. L. Patey. Controlling iterated jumps of solutions to combinatorial problems
    Computability, 6 (2017), no. 1, 47--78.
  34. L. Patey. Open questions about Ramsey-type statements in reverse mathematics
    Bulletin of Symbolic Logic, 22 (2016), no. 2, 151--169.
  35. L. Patey. The strength of the tree theorem for pairs in reverse mathematics
    Journal of Symbolic Logic, 81 (2016), no. 4, 1481--1499.
  36. L. Patey. Iterative forcing and hyperimmunity in reverse mathematics
    Computability, 6 (2017), no. 3, 209--221.
  37. L. Patey. Ramsey-type graph coloring and diagonal non-computability
    Archive for Mathematical Logic 54 (2015), no. 7-8, 899--914
  38. L. Patey. Degrees bounding principles and universal instances in reverse mathematics
    Annals of Pure and Applied Logic 166 (2015), no. 11, 1165--1185.
  39. 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
    Lecture Notes in Computer Science (2016) pp.353--363
  2. L. Patey. Iterative forcing and hyperimmunity in reverse mathematics
    Lecture Notes in Computer Science (2015) pp. 291--301 (Best student paper award)
  3. L. Patey. The complexity of satisfaction problems in reverse mathematics
    Lecture Notes in Computer Science (2014) pp. 333--342 (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. Q. Le Houérou, L. Levy Patey and K. Yokoyama. Pi04 conservation of Ramsey's theorem for pairs
  2. Q. Le Houérou, L. Levy Patey and A. Mimouni. The reverse mathematics of the pigeonhole hierarchy
  3. J. Cervelle, W. Gaudelier and L. Levy Patey. Cross-constraint basis theorems and products of partitions
  4. L. Carlucci, O. Gjetaj, Q. Le Houérou and L. Levy Patey. Ramsey-like theorems for the Schreier barrier

Ongoing projects

  1. Combinatorial weaknesses of Ramseyan principles (draft)
  2. 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. 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