7 citations · 20 across the 8 of their papers we have counts for
4 papers · 1 filter
On flexible sequences
Bruno Dinis, Tran Van Nam, Imme van den Berg
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the clas…
Axiomatics for the external numbers of nonstandard analysis
Bruno Dinis, Imme van den Berg
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stabilit…
Characterization of distributivity in a solid
Bruno Dinis, Imme van den Berg
We give a characterization of the validity of the distributive law in a solid. There exists equivalence between the characterization and the modified axiom of distibutivity valid i…
On the quotient class of non-archimedean fields
Bruno Dinis, Imme van den Berg
The quotient class of a non-archimedean field is the set of cosets with respect to all of its additive convex subgroups. The algebraic operations on the quotient class are the Mink…