Introduction to Set Shaping Theory

Introduction to Descriptive Set Theory

Mathematicians in the early 20th century discovered that the Axiom of Choice implied the existence of pathological subsets of the real line lacking desirable regularity properties (for example nonmeasurable sets). This gave rise to descriptive set theory, a systematic study of classes of sets where these pathologies can be avoided, including, in particular, the definable sets. In the first half...

SET THEORY An Introduction to Independence Proofs

A Brief Introduction to Algebraic Set Theory

This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result ...

A Quick Introduction to Basic Set Theory

This note is intended to quickly introduce basic notions in set theory to (undergraduate) students in mathematics not necessarily specializing in logic, thus requiring no background. It uses the sections on well-orderings, ordinals and cardinal arithmetic of [Kun83], as well as some parts from [Mos06].

Une introduction à la Set-Theory

Cet article se propose d'introduire les concepts de base de la Set-Theory aussi bien dans l'approche « classique » d'Allen Forte que dans les développements récents de la théorie « transformationnelle » de David Lewin. Malgré l'abondance de publications autour de la Set-Theory dans les Universités et les centres de recherche Nord-américains, cette approche reste souvent peu connue en Europe dan...