## 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