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Local induction and provably total computable functions

✍ Scribed by Cordón-Franco, Andrés; Lara-Martín, F. Félix

Book ID
122309044
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
769 KB
Volume
165
Category
Article
ISSN
0168-0072

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✍ Saeed Salehi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB

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We prove the following theorem: Let cp(z) be a formula in the language of the theory PAof discretely ordered commutative rings with unit of the form 3 y p ' ( z , y ) with 'p' E Ao and let f, : N -+ R be such that f,(z) = y iff cp'(z, y) & (Vz < y) ~( p ' ( z , 2 ) . If ITIF I -(Vz 2 0) cp(z), then