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Alternative set theory with elementary classes

Nando Prati (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Analyse relative

Yves Peraire (1992)

Annales scientifiques de l'Université de Clermont. Mathématiques

Arithmetization of the field of reals with exponentiation extended abstract

Sedki Boughattas, Jean-Pierre Ressayre (2008)

RAIRO - Theoretical Informatics and Applications


 (1) Shepherdson proved that a discrete unitary commutative semi-ring A+ satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let T range over axiom systems for ordered fields with exponentiation; for three values of T we provide a theory T in the language of rings plus exponentiation such that the ...

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