5 found
  1.  12
    Classical Consequences of Continuous Choice Principles From Intuitionistic Analysis.François G. Dorais - 2014 - Notre Dame Journal of Formal Logic 55 (1):25-39.
  2.  17
    Comparing the Strength of Diagonally Nonrecursive Functions in the Absence of Induction.François G. Dorais, Jeffry L. Hirst & Paul Shafer - 2015 - Journal of Symbolic Logic 80 (4):1211-1235.
    We prove that the statement “there is aksuch that for everyfthere is ak-bounded diagonally nonrecursive function relative tof” does not imply weak König’s lemma over${\rm{RC}}{{\rm{A}}_0} + {\rm{B\Sigma }}_2^0$. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that everyk-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of${\rm{I\Sigma }}_2^0$.
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  3.  11
    On the Indecomposability of $\Omega^{N}$.Jared R. Corduan & François G. Dorais - 2012 - Notre Dame Journal of Formal Logic 53 (3):373-395.
    We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal $\omega$ . Four natural formulations are presented, and their relative strengths are compared. In the analysis of the pigeonhole principle for $\omega^{2}$ , we uncover two weak variants of Ramsey’s theorem for pairs.
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    A Variant of Mathias Forcing That Preserves {\ Mathsf {ACA} _0}.François G. Dorais - 2012 - Archive for Mathematical Logic 51 (7-8):751-780.
    We present and analyze ${F_\sigma}$ -Mathias forcing, which is similar but tamer than Mathias forcing. In particular, we show that this forcing preserves certain weak subsystems of second-order arithmetic such as ${\mathsf{ACA}_0}$ and ${\mathsf{WKL}_0 + \mathsf{I}\Sigma^0_2}$ , whereas Mathias forcing does not. We also show that the needed reals for ${F_\sigma}$ -Mathias forcing (in the sense of Blass in Ann Pure Appl Logic 109(1–2):77–88, 2001) are just the computable reals, as opposed to the hyperarithmetic reals for Mathias forcing.
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  5.  3
    When Does Every Definable Nonempty Set Have a Definable Element?François G. Dorais & Joel David Hamkins - 2019 - Mathematical Logic Quarterly 65 (4):407-411.
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