Non-classical analysis: Difference between revisions

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Revision as of 14:04, 30 November 2009

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*Abstract Stone duality<ref>[http://www.PaulTaylor.EU/ASD Paul Taylor's site]</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 [[infinitesimals]] and allows the resulting calculus to be applied to continuous domains without local Euclidean structure as well as discrete domains.

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

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

*[[Non-Newtonian calculus]], which provides alternatives to the classical calculus of Newton and Leibniz.

*[[Non-standard analysis]], develops rigorous infinitesmals within a new number system along with a transfer principle allowing them to be applied back to the real numbers.