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.

- L. Liu and L. Patey.
The reverse mathematics of the Thin Set and Erdos-Moser theorems

*Journal of Symbolic Logic*, to appear. - B. Monin and L. Patey.
SRT22 does not imply RT22 in omega-models

*Advances in Mathematics*, to appear. - 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*, to appear. - 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. - L. Patey. Ramsey-like theorems and moduli of computation

*Journal of Symbolic Logic*, to appear. - R. Downey,
N. Greenberg,
M. Harrison-Trainor, L. Patey and
D. Turetsky

Relationships between computability-theoretic properties of problems

*Journal of Symbolic Logic*, to appear. - B. Monin, L. Patey.
The weakness of the pigeonhole principle under hyperarithmetical reductions

*Journal of Mathematical Logic*, 21 (2021), no.3, pp. 2150013, 41. - D. D. Dzhafarov and L. Patey.
COH, SRT22, and multiple functionals

*Computability*, 10 (2021), no. 2, pp. 111--121. - 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. - P. Cholak, L. Patey.
Thin set theorems and cone avoidance

*Transactions of the AMS*, 373 (2020), no. 4, 2743--2773. - 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. - B. Monin, L. Patey.
Pigeons do not jump high

*Advances in Mathematics*, 352, (2019), 1066--1095. - 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. - L. Liu,
B. Monin, and L. Patey.
A computable analysis of variable words theorems

*Proceedings of the AMS*, 147 (2019), no. 2, 823--834. - K. Yokoyama, L. Patey.
The proof-theoretic strength of Ramsey's theorem for pairs and two colors

*Advances in Mathematics*, 330 (2018), 1034--1070. - D. D. Dzhafarov, L. Patey.
Coloring trees in reverse mathematics

*Advances in Mathematics*, 318 (2017), 497--514. - L. Patey. Partial orders and immunity in reverse mathematics

*Computability*, 7 (2018) no. 4, 323--339. - L. Patey. The reverse mathematics of non-decreasing subsequences

*Archive for Mathematical Logic*, 56 (2017), no. 5-6, 491--506. - L. Patey.
Dominating the Erdos-Moser theorem in reverse mathematics

*Annals of Pure and Applied Logic*, 168 (2017), no. 6, 1172--1209. - B. Monin, L. Patey.
Pi01 encodability and omniscient reductions

*Notre Dame Journal of Formal Logic*, 60 (2019), no. 1, 1--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* - E. Frittaion and L. Patey.
Coloring the rationals in reverse mathematics

*Computability*, 6 (2017), no. 4, 319--331. - 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. - 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* - L. Bienvenu
and L. Patey. Diagonally non-computable functions and fireworks

*Information and Computation*, 253 (2017), part 1, 64--77. - L. Patey.
Controlling iterated jumps of solutions to combinatorial problems

*Computability*, 6 (2017), no. 1, 47--78. - L. Patey.
Open questions about Ramsey-type statements in reverse mathematics

*Bulletin of Symbolic Logic*, 22 (2016), no. 2, 151--169. - L. Patey.
The strength of the tree theorem for pairs in reverse mathematics

*Journal of Symbolic Logic*, 81 (2016), no. 4, 1481--1499. - L. Patey.
Iterative forcing and hyperimmunity in reverse mathematics

*Computability*, 6 (2017), no. 3, 209--221. - L. Patey. Ramsey-type graph coloring and diagonal non-computability

*Archive for Mathematical Logic*54 (2015), no. 7-8, 899--914 - L. Patey.
Degrees bounding principles and universal instances in reverse mathematics

*Annals of Pure and Applied Logic*166 (2015), no. 11, 1165--1185. - L. Patey.
The complexity of satisfaction problems in reverse mathematics

*Computability*, 4(1):69–84, 2015.

- L. Patey.
Partial orders and immunity in reverse mathematics

*Lecture Notes in Computer Science*(2016) pp.353--363 - L. Patey.
Iterative forcing and hyperimmunity in reverse mathematics

*Lecture Notes in Computer Science*(2015) pp. 291--301 (Best student paper award) - L. Patey.
The complexity of satisfaction problems in reverse mathematics

*Lecture Notes in Computer Science*(2014) pp. 333--342 (Best student paper award) - 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.*

- B. Monin and L. Patey. Partition genericity and pigeonhole basis theorems

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

- L. Patey. The reverse mathematics of Ramsey-type theorems
*Ph.D thesis. 2016* - L. Patey. Somewhere over the rainbow Ramsey theorem for pairs. 2015
- L. Patey. A note on "Separating principles below Ramsey's theorem for pairs" 2013
- L. Patey.
Reverse Mathematics and a Weak Ramsey-Type König’s Lemma.
*Internship report. 2012* - L. Patey.
CPS Transformation of Lisp-Like Multi-Staged Languages
*Extended version. 2011* - L. Patey. Eternity II et variantes.
*Internship report. 2010*