Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer (T), Idealization (I), and Standardization (S). We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of nonstandard asymptotics.</p
We give an axiomatic framework for getting full elementary extensions such as ultrapowers. From five...
ACL2(r) is a variant of ACL2 that supports the irrational real and complex numbers. Its logical foun...
A nonstandard set theory *ZFC is proposed that axiomatizes the nonstandard embedding *. Besides the ...
Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom sche...
AbstractVan den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 (1992) 73–92. I...
Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom sche...
Although epsilon-delta analysis has enjoyed great success in giving rigor to modern mathematics, non...
We determine sufficient structure for an elementary topos to emulate E. Nelson's Internal Set Theory...
Abstract. The principal set-theoretic credos of nonstandard analysis are presented. A “naive ” justi...
AbstractWe study models ofHST (a nonstandard set theory which includes, in particular, the Replaceme...
This thesis provides a framework to make sense of models of E. Nelson’s Internal Set Theory (and hen...
"Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Int...
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective,...
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is t...
In practice we do not always need to be exact. We may ignore small quantities and be happy with appr...
We give an axiomatic framework for getting full elementary extensions such as ultrapowers. From five...
ACL2(r) is a variant of ACL2 that supports the irrational real and complex numbers. Its logical foun...
A nonstandard set theory *ZFC is proposed that axiomatizes the nonstandard embedding *. Besides the ...
Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom sche...
AbstractVan den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 (1992) 73–92. I...
Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom sche...
Although epsilon-delta analysis has enjoyed great success in giving rigor to modern mathematics, non...
We determine sufficient structure for an elementary topos to emulate E. Nelson's Internal Set Theory...
Abstract. The principal set-theoretic credos of nonstandard analysis are presented. A “naive ” justi...
AbstractWe study models ofHST (a nonstandard set theory which includes, in particular, the Replaceme...
This thesis provides a framework to make sense of models of E. Nelson’s Internal Set Theory (and hen...
"Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Int...
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective,...
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is t...
In practice we do not always need to be exact. We may ignore small quantities and be happy with appr...
We give an axiomatic framework for getting full elementary extensions such as ultrapowers. From five...
ACL2(r) is a variant of ACL2 that supports the irrational real and complex numbers. Its logical foun...
A nonstandard set theory *ZFC is proposed that axiomatizes the nonstandard embedding *. Besides the ...
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