Models of arithmetic and upper Bounds for arithmetic sets
Journal of Symbolic Logic 59 (3):977-983 (1994)
| Abstract | We settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions | |||||||||
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Michael Potter (1998). Classical Arithmetic as Part of Intuitionistic Arithmetic. Grazer Philosophische Studien 55:127-41.
Richard Pettigrew (2010). The Foundations of Arithmetic in Finite Bounded Zermelo Set Theory. Cahiers du Centre de Logique 17:99-118.
Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
Harold T. Hodes (1981). Upper Bounds on Locally Countable Admissible Initial Segments of a Turing Degree Hierarchy. Journal of Symbolic Logic 46 (4):753-760.
Charles McCarty (2013). Paradox and Potential Infinity. Journal of Philosophical Logic 42 (1):195-219.
George Mills & Jeff Paris (1984). Regularity in Models of Arithmetic. Journal of Symbolic Logic 49 (1):272-280.
Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
Alistair H. Lachlan & Robert I. Soare (1998). Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets. Journal of Symbolic Logic 63 (1):59-72.
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