Institute for Discrete Mathematics and Geometry

Vienna University of Technology

*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]

*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]