Addendum to “A note on the MacDowell–Specker theorem”
Addendum to "Hyperdefinite stochastic integration III".
Addition of initial segments. I.
Addition of initial segments. II.
Alternative set theory with elementary classes
In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.
An application of nonstandard analysis to functional equations.
An elimination of infinitely small quantities and infinitely large numbers (within the framework of AST)
An elimination of the predicate “to be a standard member” in nonstandard models of arithmetic
An operator equation and relativistic alterations in the time of radioactive decay.
An Ordering of the set of Sentences of Peano Arithmetic
Analyse relative
Approximation diophantienne et distances ultramétriques non standard
Arithmetic of cuts and cuts of classes
Arithmetically independent integers and values of rational functions.
Arithmetization of the field of reals with exponentiation extended abstract
(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 in the language of rings plus exponentiation such that the ...
Asymptotique dans un corps de Hardy
Axiomatic foundations for Nonstandard Analysis
Biequivalence vector spaces in the alternative set theory
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...
Boolean powers and stochastic spaces
Borel classes in AST. Measurability, cuts and equivalence