A structured visual guide to the major mathematical areas and their relationships.
Search by code, branch, topic, subtopic, or a keyword from the descriptions.
This subtopic investigates nonstandard models and methods that extend classical mathematical frameworks with infinitesimal or alternative structures. It is used to analyze standard theories from new viewpoints, simplify arguments, and study models of arithmetic and analysis with different internal properties. Applications include logic, analysis, probability, and mathematical economics where nonstandard techniques offer elegant formulations or proofs.
This topic covers nonstandard models in mathematics, especially models built using ultraproducts and transfer principles. It underpins nonstandard analysis and alternative treatments of arithmetic and analysis.
Nonstandard analysis (Wikipedia)
Used to reformulate analysis with infinitesimal methods and to study alternative model-theoretic viewpoints.
This topic covers other applications of nonstandard models, including uses in economics, probability, and analysis beyond the foundational theory itself. It captures the applied side of nonstandard techniques.
Nonstandard analysis applications (Wikipedia)
Used to apply nonstandard methods in areas where infinitesimal reasoning clarifies or shortens proofs.
This topic covers nonstandard models of arithmetic, especially nonstandard extensions of the natural numbers and arithmetic theories. It is a classic area of model theory and foundations.
Nonstandard model of arithmetic (Wikipedia)
Used to study the model theory of arithmetic and to illuminate independence and interpretability questions.