•  38
    On the existence of small antichains for definable quasi-orders
    with Raphaël Carroy and Zoltán Vidnyánszky
    Journal of Mathematical Logic 21 (2): 2150005. 2021.
    We generalize Kada’s definable strengthening of Dilworth’s characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.
  •  36
    We generalize the [Formula: see text] dichotomy to doubly-indexed sequences of analytic digraphs. Under a mild definability assumption, we use this generalization to characterize the family of Borel actions of tsi Polish groups on Polish spaces that can be decomposed into countably-many Borel actions admitting complete Borel sets that are lacunary with respect to an open neighborhood of the identity. We also show that if the group in question is non-archimedean, then the inexistence of such a de…Read more
  •  67
    I argue that we cannot fully understand Aristotle’s position on political stability and state preservation in the Politics with paying close attention to his Eudemian Ethics. We learn from considering the Politics and the Eudemian Ethics in concert that even ‘correct’ regimes are unstable when citizens do not possess full virtue. Aristotle introduces his formal account of the knowledge requirements for virtue in Eudemian Ethics 8.3, and he applies these knowledge requirements as an explanation f…Read more
  •  37
    Recurrence and the existence of invariant measures
    with Manuel J. Inselmann
    Journal of Symbolic Logic 86 (1): 60-76. 2021.
    We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact Polish group on a standard Borel space satisfies such a condition but does not have an orbit supporting an invariant Borel probability measure, then there is an invariant Borel set on which the action satisfies the condition but does not have an invariant Borel probability measure.
  •  20
    Bases for functions beyond the first baire class
    with Raphaël Carroy
    Journal of Symbolic Logic 85 (3): 1289-1303. 2020.
    We provide a finite basis for the class of Borel functions that are not in the first Baire class, as well as the class of Borel functions that are not $\sigma $ -continuous with closed witnesses.
  •  15
    On the existence of large antichains for definable quasi-orders
    with Zoltán Vidnyánszky
    Journal of Symbolic Logic 85 (1): 103-108. 2020.
    We simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.
  •  24
    Measurable perfect matchings for acyclic locally countable borel graphs
    with Clinton T. Conley
    Journal of Symbolic Logic 82 (1): 258-271. 2017.