My papers (with abstracts)

• The \(\kappa\)-Strongly Proper Forcing Axiom, with Sean Cox, Asaf Karagila, and Christoph Weiss. Submitted (2024). pdf


• On forcibility of \(\Sigma_2\) sentences over \(L(V_\delta)\). To appear in RIMS Kokyuroku proceedings series (2023). pdf


• Consistent and inconsistent generalizations of Martin's Axiom, weak square, and weak Chang's Conjecture, with Nutt Tananimit. Submitted. pdf


• PFA for \(\aleph_1\)-sized posets, Prikty-type proper forcing, and the size of the continuum, with Mohammad Golshani. Submitted. pdf


• Few new reals, with Miguel Ángel Mota. To appear in Journal of Mathematical Logic, 2024. pdf


• Martin's Maximum\({}^{++}\) implies Woodin's axiom \((*)\), with Ralf Schindler, Annals of Mathematics, vol. 193, no. 3 (2021), pp. 793-835. pdf


• The special Aronszajn tree property at \(\aleph_2\) and GCH, with Mohammad Golshani. Submitted pdf


• Parametrized Measuring and Club Guessing, with John Krueger, Fundamenta Mathematicae, vol. 249 (2020), 169-183. pdf


• Dependent choice, properness, and generic absoluteness, with Asaf Karagila, The Review of Symbolic Logic, vol. 14, no. 1 (2021), pp. 225-249. pdf


• Incompatible bounded category forcing axioms, with Matteo Viale, Journal of Mathematical Logic, vol. 22, no. 2, 2250006 (2022). pdf


• Reducibility of equivalence relations arising from non-stationary ideals under large cardinal assumptions, with Tapani Hyttinen, Vadim Kulikov, and Miguel Moreno. In Notre Dame Journal of Formal Logic, vol. 60 (2019), no. 4, 665-682.


• A forcing notion collapsing \(\aleph_3\) and preserving all other cardinals, The Journal of Symbolic Logic, vol. 83, no. 4 (2018), 1579-1594. pdf


• Long reals, with Konstantinos Tsaprounis. In Journal of Logic and Analysis, vol. 10 (2018), no 1, 36 pp. pdf


• Adding many Baumgartner clubs, Archive for Mathematical Logic, vol. 56 (7) (2017), no. 7-8, 797-810. pdf


• The consistency of a club-guessing failure at the successor of a regular cardinal. In "Infinity, computability, and metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch,'' S. Geschke, B. Löwe and P. Schlicht, eds., College Publications, Tributes 23, London, 2014, 5-27. pdf


• Separating club-guessing principles in the presence of fat forcing axioms, with Miguel Ángel Mota, Annals of Pure and Applied Logic, vol. 167, 3 (2016), 284-308. pdf


• Forcing lightface definable well-orders without the CGH, with Peter Holy and Philipp Lücke. In Annals of Pure and Applied Logic, vol. 166, 5 (2015), 553-582. pdf


• A generalization of Martin's Axiom, with Miguel Ángel Mota. In Israel Journal of Mathematics, vol. 210 (2015), 193-231. pdf


• Forcing consequences of PFA together with the continuum large, with Miguel Ángel Mota. Transactions of the AMS, vol. 367 (2015), 6103-6129. pdf


• Relative definability. RIMS Kokyuroku Bessatsu 1895 (2014), 1-11. pdf


• Bounded Martin's Maximum with an asterisk, with Ralf Schindler. Notre Dame Journal of Formal Logic, vol. 55, 3 (2014), 333-348. pdf


• Bounded forcing axioms and Baumgartner's conjecture, with Sy D. Friedman, Miguel Angel Mota, and Marcin Sabok. Annals of Pure and Applied Logic, vol. 164, 12 (2013), 1178-1186. pdf


• Forcing axioms and the Continuum Hypothesis, with Paul B. Larson and Justin T. Moore. Acta Mathematica, vol. 210 (2013), 1-29. Journal link.


• Definable well-orders of \(H(\omega_2)\) and GCH, with Sy D. Friedman, The Journal of Symbolic Logic, vol. 77, 4 (2012), 1101-1121. JSTOR link, pdf


• On a convenient property about \([\gamma]^{\aleph_0}\), Archive for Mathematical Logic, vol. 48, 7 (2009), 653-677. pdf


• Forcing notions in inner models, Archive for Mathematical Logic, vol. 48, 7 (2009), 643-651. pdf


• Dense non-reflection for stationary collections of countable sets, with John Krueger and Yasuo Yoshinobu. Annals of Pure and Applied Logic, vol. 161 (2009), 94-108. pdf


• Large cardinals and locally defined well-orders of the universe, with Sy D. Friedman. Annals of Pure and Applied Logic, vol. 157 (2009), 1-15.


• Guessing and non-guessing of canonical functions, Annals of Pure and Applied Logic, vol. 146 (2007), 150-179. pdf


• Coding into \(H(\omega_2)\) together (or not) with forcing axioms. A survey, in Computational prospects of infinity. Part II, Institute of Math. Sciences, Natl. Univ. of Singapore, Lecture Notes Series Vol. 15. Singapore, 2008, 23-46. pdf


• Coding by club-sequences, Annals of Pure and Applied Logic, vol. 142, 1-3 (2006), 98-114.


• Generic absoluteness for \(\Sigma_1\) formulas and the continuum problem, in Logic Colloquium 2002, Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, Wellesley, Massachusetts, 2006, 1-27.


• The nonexistence of robust codes for subsets of \(\omega_1\), Fundamenta Mathematicae, vol. 186, 3 (2005), 215-231. pdf


• Bounded forcing axioms and the size of the continuum, in Logic Colloquium 2000, Lecture Notes in Logic, vol. 19, Association for Symbolic Logic, Wellesley, Massachusetts, 2005, 211-227.


• On simple partitions of \([\kappa]^{\kappa}\), Fundamenta Mathematicae, vol. 177, 2 (2003), 139-149. pdf


• Bounded Martin's Maximum, weak Erd\H{o}s cardinals, and \(\psi_{AC}\), with Philip D. Welch. The Journal of Symbolic Logic, vol. 67, 3 (2002), 1141-1152. JSTOR link.


• A maximal bounded forcing axiom, The Journal of Symbolic Logic, vol. 67, 1 (2002), 130-142. JSTOR link.


• Bounded forcing axioms and the continuum, with Joan Bagaria. Annals of Pure and Applied Logic, vol. 109, 3 (2001), 179-203.