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The shortest definition of a number in Peano arithmetic
Mathematical Logic Quarterly 49 (1):83-86 (2003)
Abstract
The shortest definition of a number by a first order formula with one free variable, where the notion of a formula defining a number extends a notion used by Boolos in a proof of the Incompleteness Theorem, is shown to be non computable. This is followed by an examination of the complexity of sets associated with this functionMy notes
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Citations of this work
On proofs of the incompleteness theorems based on Berry's paradox by Vopěnka, Chaitin, and Boolos.Makoto Kikuchi, Taishi Kurahashi & Hiroshi Sakai - 2012 - Mathematical Logic Quarterly 58 (4-5):307-316.
On constructivity and the Rosser property: a closer look at some Gödelean proofs.Saeed Salehi & Payam Seraji - 2018 - Annals of Pure and Applied Logic 169 (10):971-980.
References found in this work
A Note on Boolos' Proof of the Incompleteness Theorem.Makoto Kikuchi - 1994 - Mathematical Logic Quarterly 40 (4):528-532.
The false assumption underlying berry's paradox.James D. French - 1988 - Journal of Symbolic Logic 53 (4):1220-1223.
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