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Creators/Authors contains: "Towsner, Henry"

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  1. ; (, Canadian Mathematical Bulletin)
    Abstract For which choices of$$X,Y,Z\in \{\Sigma ^1_1,\Pi ^1_1\}$$does no sufficiently strongX-sound andY-definable extension theory prove its ownZ-soundness? We give a complete answer, thereby delimiting the generalizations of Gödel’s second incompleteness theorem that hold within second-order arithmetic. 
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    Free, publicly-accessible full text available July 24, 2026
  2. ; (, Proceedings of the 14th Panhellenic Logic Symposium)
    Kavvos, Alex; Gregoriades, Vassilis (Ed.)
    For n∈ℕ and ε>0, given a sufficiently long sequence of events in a probability space all of measure at least ε, some n of them will have a common intersection. A more subtle pattern: for any 0<1, we cannot find events Ai and Bi so that μ(Ai∩Bj)≤p and μ(Aj∩Bi)≥q for all 1 
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    Accepted Manuscript Full Text Available
  3. ; (, 14th Panhellenic Logic Symposium)
    For n ∈ N and ε > 0, given a sufficiently long sequence of events in a probability space all of measure at least ε, some n of them will have a common intersection. A more subtle pattern: for any 0 < p < q < 1, we cannot find events Ai and Bi so that μ (Ai ∩ Bj ) ≤ p and μ (Aj ∩ Bi ) ≥ q for all 1 < i < j < n, assuming n is sufficiently large. This is closely connected to model-theoretic stability of probability algebras. We survey some results from our recent work in [7] on more complicated patterns that arise when our events are indexed by multiple indices. In particular, how such results are connected to higher arity generalizations of de Finetti’s theorem in probability, structural Ramsey theory, hypergraph regularity in combinatorics, and model theory. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Journal of Mathematical Logic)
    We characterize the completely determined Borel subsets of HYP as exactly the [Formula: see text] subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this answers a question of Astor, Dzhafarov, Montalbán, Solomon and the third author. 
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