# William Chan

###
Postdoctoral Associate

Department of Mathematics

Carnegie Mellon University

#### Contact Information

__Office__: Wean Hall

__Email__: See end of a recent paper for a CMU email address.

__Curriculum Vitae__: CV

#### Teaching

#### Papers

*A Wadge Determinacy Principle Equivalent to Weak König Lemma*. Submitted. [pdf]
*Equivalence of Codes for Countable Sets of Reals*. Submitted. [pdf]
*More Definable Combinatorics around the First and Second Uncountable Cardinal*. With Stephen Jackson and Nam Trang. Submitted. [pdf]
*Definable Combinatorics at the First Uncountable Cardinal*. With Stephen Jackson. To appear in *Transactions of the American Mathematical Society*. [pdf]
*Applications of Infinity-Borel Codes to Definability and Definable Cardinals*. With Stephen Jackson. Submitted. [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.* To appear in *Journal of Mathematical Logic*. [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. To appear in *Israel Journal of Mathematics*. [pdf][arXiv]
*Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations.* With Stephen Jackson. Submitted. [pdf][arXiv]
*L(R) with Determinacy Satisfies the Suslin Hypothesis.* With Stephen Jackson. *Advances in Mathematics*, 346 (2019), 305-328. [pdf][arXiv]
*Scott Ranks of Classifications of the Admissibility Equivalence Relation.* With Matthew Harrison-Trainor and Andrew Marks. Submitted. [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. Submitted. [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.* *The Journal of Symbolic Logic*, 82 (2017), 893-930. [pdf][arXiv]

#### Notes

*The Clopen Partition Property.* With Stephen Jackson. [pdf]
*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]