Abstract
In connection with uniform computability and intuitionistic provability, the strength of the sequential version of \({\rm \Pi^1_2}\) theorems has been investigated in reverse mathematics. In some examples, we illustrate that it occasionally depends on the way of formalizing the \({\rm \Pi^1_2}\) statement, so the investigation of sequential strength demands careful attention to the formalization. Moreover our results suggest the optimality of Dorais’s uniformization theorems.
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Fujiwara, M., Yokoyama, K. (2013). A Note on the Sequential Version of \({\rm \Pi^1_2}\) Statements. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_20
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DOI: https://doi.org/10.1007/978-3-642-39053-1_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39052-4
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