Papers
The weakness of finding descending sequences in ill-founded linear orders
Work in progress with Arno Pauly and Manlio Valenti
A subset of this has appeared in the Computability in Europe (CiE) 2024 proceedings
Redundancy of information: lowering dimension
With Joseph Miller, Mariya Soskova, Linda Brown Westrick
Halin’s infinite ray theorems: complexity and reverse mathematics: Version E
With James S. Barnes and Richard A. Shore
A version of this will appear in the Journal of Mathematical Logic
PA relative to an enumeration oracle
With Iskander Kalimullin, Joseph Miller, Mariya Soskova
Journal of Symbolic Logic, vol. 88, Issue 4, December 2023, pp. 1497 – 1525
The strength of an axiom of choice for branches in trees
Journal of Symbolic Logic, vol. 88, Issue 4, December 2023, pp. 1367 – 1386
Extensions of two constructions of Ahmad
With Steffen Lempp, Keng Meng Ng, Mariya Soskova
Computability, vol. 11, no. 3-4, pp. 269-297, 2022
Theorems of Hyperarithmetic Analysis and Almost Theorems of Hyperarithmetic Analysis
With James S. Barnes and Richard A. Shore
Bulletin of Symbolic Logic, vol. 28, Issue 1, pp. 133-149, March 2022
(This communication reports on “The strength of an axiom of choice for branches in trees”, “”Halin’s infinite ray theorems: complexity and reverse mathematics” as well as “Almost theorems of hyperarithmetic analysis” by Richard A. Shore.)
Finding descending sequences through ill-founded linear orders
With Arno Pauly and Manlio Valenti
Journal of Symbolic Logic, vol. 86, no. 2, pp. 817-854, 2021
Caution: This paper contains some incorrect results on bad sequences; please see the beginning of the arXiv pdf
Some computability-theoretic reductions between principles around ATR_0
Part of this has appeared in Annals of Pure and Applied Logic vol. 171 no. 6 2020 under the title Embeddings between well-orderings: Computability-theoretic reductions.
Ramsey’s theorem and products in the Weihrauch degrees
With Damir D. Dzhafarov, Denis R. Hirschfeldt, Ludovic Patey, Arno Pauly
Computability vol. 9, no. 2, pp. 85-110, 2020
Compositions of multi-valued functions
Computability vol. 9, no. 3-4, pp. 231-247, 2020
Notes and Talks
Uniform distribution and algorithmic randomness (Computability in Europe, July 2024): slides
Expository slides on Hilbert’s 10th problem (NUS Summer Science Institute, July 2024): slides
Interior operators in the Weihrauch lattice (World Logic Day event organized by Department of Mathematics, Nazarbayev University and Mathematical Center, Akademgorodok, Jan 2024): slides, youtube
Reductions and (resolvable) combinatorial designs (Asian Logic Conference, Tianjin, China, Oct 2023): slides
Redundancy of information: Lowering effective dimension (19th International Conference on Computability and Complexity in Analysis, May 2022): slides
Extensions of embeddings in the Sigma^0_2 enumeration degrees (Association of Symbolic Logic North American Annual Meeting, Cornell, April 2022): slides, youtube of a different talk on the same topic
Pi^0_1 classes relative to an enumeration oracle (New directions in computability theory, Luminy, March 2022): slides
Expository slides on Hilbert’s 10th problem (Logic Association of Malaysia Introductory Logic Course, February 2022): slides, youtube part 1, youtube part 2, youtube part 3
Inseparable pairs and recursion theory (Boise Extravaganza in Set Theory, June 2021): slides
Computing descending sequences in linear orderings (Computability Theory and Applications Online Seminar, Aug 2020): slides, youtube
A Sigma^1_1 axiom of finite choice and Steel forcing (Workshop on Digitalization and Computable Models, virtual in Novosibirsk, July 2020): slides
I wrote some notes for a topics course on Weihrauch reducibility: notes
My PhD thesis, supervised by Richard A. Shore: thesis
A theorem of Halin and hyperarithmetic analysis (ASL North American Annual Meeting, New York, NY, May 2019): slides
Some reductions between theorems around ATR_0 (Computability Theory and Applications, Waterloo, Canada, June 2018): slides
Compositions of multivalued functions (Asian Logic Conference, Daejeon, Korea, July 2017): slides