Non-classical analysis: Difference between revisions

Revision as of 17:49, 4 October 2013

Revision as of 19:48, 4 December 2017

Line 4:

*Abstract Stone duality,<ref>{{cite web|url=http://www.PaulTaylor.EU/ASD |title=Paul Taylor's site |publisher=Paultaylor.eu |date= |accessdate=2013-09-23}}</ref> a programme to re-axiomatise [[general topology]] ''directly'', instead of using [[set theory]]. It is formulated in the style of [[type theory]] and is in principle computable. It is currently able to characterise the [[category (mathematics)|category]] of (not necessarily Hausdorff) computably based locally compact spaces. It allows the development of a form of constructive real analysis using topological rather than [[Cauchy sequence|metrical]] arguments.

*[[Chainlet geometry]], a recent development of geometric integration theory which incorporates [[infinitesimalsinfinitesimal]]s and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains.

*[[Constructive analysis]], which is built upon a foundation of [[constructive logic|constructive]], rather than classical, logic and set theory.

*[[Intuitionistic analysis]], which is developed from constructive logic like constructive analysis but also incorporates [[choice sequence]]s.

Line 11:

*[[Smooth infinitesimal analysis]], which is developed in a smooth topos.

[[Non-standard analysis]] and the calculus it involves, [[non-standard calculus]], are considered part of [[classical mathematics]] (i.e. The concept of "[[hyperreal number]]" it uses, can be constructed in the framework of [[Zermelo-FraenkelZermelo–Fraenkel set theory]]).

==References==