7 found
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Linda Westrick [5]Linda Brown Westrick [3]
  1.  19
    The determined property of baire in reverse math.Eric P. Astor, Damir Dzhafarov, Antonio Montalbán, Reed Solomon & Linda Brown Westrick - 2020 - Journal of Symbolic Logic 85 (1):166-198.
    We define the notion of a completely determined Borel code in reverse mathematics, and consider the principle $CD - PB$, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than $AT{R_0}$. Any ω-model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω-model (...)
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  2.  18
    A lightface analysis of the differentiability rank.Linda Brown Westrick - 2014 - Journal of Symbolic Logic 79 (1):240-265.
  3.  19
    A Topological Approach to Undefinability in Algebraic Extensions Of.Kirsten Eisenträger, Russell Miller, Caleb Springer & Linda Westrick - 2023 - Bulletin of Symbolic Logic 29 (4):626-655.
    For any subset $Z \subseteq {\mathbb {Q}}$, consider the set $S_Z$ of subfields $L\subseteq {\overline {\mathbb {Q}}}$ which contain a co-infinite subset $C \subseteq L$ that is universally definable in L such that $C \cap {\mathbb {Q}}=Z$. Placing a natural topology on the set ${\operatorname {Sub}({\overline {\mathbb {Q}}})}$ of subfields of ${\overline {\mathbb {Q}}}$, we show that if Z is not thin in ${\mathbb {Q}}$, then $S_Z$ is meager in ${\operatorname {Sub}({\overline {\mathbb {Q}}})}$. Here, thin and meager both mean “small”, (...)
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  4.  25
    (1 other version)Luzin’s (n) and randomness reflection.Arno Pauly, Linda Westrick & Liang Yu - 2020 - Journal of Symbolic Logic:1-27.
    We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have (...)
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  5.  18
    Borel combinatorics fail in HYP.Henry Towsner, Rose Weisshaar & Linda Westrick - 2022 - Journal of Mathematical Logic 23 (2).
    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 (...)
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  6.  25
    An Effective Analysis of the Denjoy Rank.Linda Westrick - 2020 - Notre Dame Journal of Formal Logic 61 (2):245-263.
    We analyze the descriptive complexity of several Π11-ranks from classical analysis which are associated to Denjoy integration. We show that VBG, VBG∗, ACG, and ACG∗ are Π11-complete, answering a question of Walsh in case of ACG∗. Furthermore, we identify the precise descriptive complexity of the set of functions obtainable with at most α steps of the transfinite process of Denjoy totalization: if |⋅| is the Π11-rank naturally associated to VBG, VBG∗, or ACG∗, and if α<ωck1, then {F∈C(I):|F|≤α} is Σ02α-complete. These (...)
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  7.  20
    Weakly 2-randoms and 1-generics in Scott sets.Linda Brown Westrick - 2018 - Journal of Symbolic Logic 83 (1):392-394.
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