uncountable set
31Generating set of a group — In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination …
32Critical point (set theory) — In set theory, the critical point of an elementary embedding of a transitive class into another transitive class is the smallest ordinal which is not mapped to itself.[1] Suppose that j : N → M is an elementary embedding where N and M are… …
33Morass (set theory) — For the variety of wetland, see marsh. In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create large structures from a small number of small approximations. They were invented by Ronald… …
34Model theory — This article is about the mathematical discipline. For the informal notion in other parts of mathematics and science, see Mathematical model. In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields,… …
35Cantor's diagonal argument — An illustration of Cantor s diagonal argument for the existence of uncountable sets. The sequence at the bottom cannot occur anywhere in the list of sequences above. Cantor s diagonal argument, also called the diagonalisation argument, the… …
36Finite intersection property — In general topology, the finite intersection property is a property of a collection of subsets of a set X . A collection has this property if the intersection over any finite subcollection of the collection is nonempty.DefinitionLet X be a set… …
37Georg Cantor — Infobox Scientist name = Georg Ferdinand Ludwig Cantor image width=225px caption = birth date = birth date|1845|3|3 birth place = Saint Petersburg, Russia death date = death date and age|1918|1|6|1845|3|3 death place = Halle, Germany residence =… …
38Löwenheim–Skolem theorem — In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… …
39First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …
40Covering lemma — See also: Jensen s covering theorem In mathematics, under various anti large cardinal assumptions, one can prove the existence of the canonical inner model, called the Core Model, that is, in a sense, maximal and approximates the structure of V.… …
