Graduate studies at Western
Journal of Symbolic Logic 58 (2):456-476 (1993)
|Abstract||Models of normal open induction (NOI) are those discretely ordered rings, integrally closed in their fraction field whose nonnegative part satisfy Peano's induction axioms for open formulas in the language of ordered semirings. Here we study the problem of representability of an element a of a model M of NOI (in some extension of M) by a quadratic form of the type X2 + bY2 where b is a nonzero integer. Using either a trigonometric or a hyperbolic parametrization we prove that except in some trivial cases, M[ x, y] with x2 + by2 = a can be embedded in a model of NOI. We also study quadratic extensions of a model M of NOI; we first prove some properties of the ring of Gaussian integers of M. Then we study the group of solutions of a Pell equation in NOI; we construct a model in which the quotient group by the squares has size continuum|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Lev D. Beklemishev (2003). On the Induction Schema for Decidable Predicates. Journal of Symbolic Logic 68 (1):17-34.
G. Gutiérrez, I. P. de Guzmán, J. Martínez, M. Ojeda-Aciego & A. Valverde (2002). Satisfiability Testing for Boolean Formulas Using Δ-Trees. Studia Logica 72 (1):85 - 112.
Morteza Moniri & Mojtaba Moniri (2002). Some Weak Fragments of HA and Certain Closure Properties. Journal of Symbolic Logic 67 (1):91-103.
Michael Mytilinaios (1989). Finite Injury and ∑1-Induction. Journal of Symbolic Logic 54 (1):38 - 49.
David Marker (1991). End Extensions of Normal Models of Open Induction. Notre Dame Journal of Formal Logic 32 (3):426-431.
Margarita Otero (1992). The Amalgamation Property in Normal Open Induction. Notre Dame Journal of Formal Logic 34 (1):50-55.
Margarita Otero (1990). On Diophantine Equations Solvable in Models of Open Induction. Journal of Symbolic Logic 55 (2):779-786.
Alessandro Berarducci & Margarita Otero (1996). A Recursive Nonstandard Model of Normal Open Induction. Journal of Symbolic Logic 61 (4):1228-1241.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?