William Chan

Postdoctoral Fellow
Institute for Discrete Mathematics and Geometry
Vienna University of Technology

Contact Information

Papers

• Cardinality of the Set of Bounded Subsets of a Cardinal. In preparation.
• Infinity-Borel Codes in Natural Models of AD⁺. With Stephen Jackson and Nam Trang. Submitted. [pdf]
• Almost Disjoint Families under Determinacy. With Stephen Jackson and Nam Trang. Advances in Mathematics, 437 (2024). [pdf]
• Definable Combinatorics of Strong Partition Cardinals. In preparation. [pdf]
• Almost Everywhere Behavior of Functions According to Partition Measures. With Stephen Jackson and Nam Trang. Forum of Mathematics, Sigma, 12 (2024): e16, 1-36. [pdf]
• Countable Length Everywhere Club Uniformization. With Stephen Jackson and Nam Trang. Journal of Symbolic Logic, 88 (2023), no. 4, 1556-1572. [pdf]
• The Size of the Class of Countable Sequences of Ordinals. With Stephen Jackson and Nam Trang. Transactions of the American Mathematical Society, 375 3 (2022), 1725-1743. [pdf]
• A Lipschitz Determinacy Principle Equivalent to Weak König Lemma. Annals of Pure and Applied Logic, 174 (2023), no 3. [pdf]
• Equivalence of Codes for Countable Sets of Reals. Canadian Mathematical Bulletin, 64, no. 3 (2021), 580-590. [pdf]
• More Definable Combinatorics around the First and Second Uncountable Cardinal. With Stephen Jackson and Nam Trang. Journal of Mathematical Logic, 23 (2023), no. 3. [pdf]
• Definable Combinatorics at the First Uncountable Cardinal. With Stephen Jackson. Transactions of the American Mathematical Society, 374 3 (2021), 2035-2056. [pdf]
• Applications of Infinity-Borel Codes to Definability and Definable Cardinals. With Stephen Jackson. Fundamenta Mathematicae, 265 (2024), 215-258. [pdf]
• Bounds on Continuous Scott Rank. With Ruiyuan Chen. Proceedings of the American Mathematical Society, 148 8 (2020), 3591-3605. [pdf][arXiv]
• Bounds on Scott Ranks of Some Polish Metric Spaces. Journal of Mathematical Logic, 21 (2021), no 1. [pdf][arXiv]
• An Introduction to Combinatorics of Determinacy. Trends in Set Theory, Contemporary Mathematics, 752 (2020), 21-75. [pdf][arXiv]
• The Destruction of the Axiom of Determinacy by Forcings on R when Theta is Regular. With Stephen Jackson. Israel Journal of Mathematics, 241 (2021), 119-138. [pdf][arXiv]
• Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations. With Stephen Jackson. Annals of Pure and Applied Logic, 172 (2021), no 8. [pdf][arXiv]
• L(R) with Determinacy Satisfies the Suslin Hypothesis. With Stephen Jackson. Advances in Mathematics, 346 (2019), 305-328. [pdf][arXiv]
• Ordinal Definability and Combinatorics of Equivalence Relations. Journal of Mathematical Logic, 19 (2019), no 2. [pdf][arXiv]
• Definable Combinatorics of Some Borel Equivalence Relations. With Connor Meehan. Submitted. [pdf][arXiv]
• When a Relation with All Borel Sections will be Borel Somewhere? With Menachem Magidor. Proceedings of the American Mathematical Society, 150 2 (2022), 833-847. [pdf][arXiv]
• The Countable Admissible Ordinal Equivalence Relation. Annals of Pure and Applied Logic, 168 (2017), 1224-1246. [pdf][arXiv]
• Equivalence Relations Which Are Borel Somewhere. Journal of Symbolic Logic, 82 (2017), no. 3, 893-930. [pdf][arXiv]

Notes

• Constructibility Level Equivalence Relation. [pdf]
• The Clopen Partition Property. With Stephen Jackson. [pdf]
• Scott Ranks of Classifications of the Admissibility Equivalence Relation. With Matthew Harrison-Trainor and Andrew Marks. [pdf][arXiv]
• Jensen's Model Existence Theorem. [pdf]
• Non-Reducibility of Isomorphism of Counterexamples to Vaught's Conjecture to the Admissibility Equivalence Relation. [pdf]
• Canonicalization by Absoluteness. [pdf]