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2. Set theory - Wikipedia

   en.wikipedia.org/wiki/Set_theory

   Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.

3. Mathematical logic - Wikipedia

   en.wikipedia.org/wiki/Mathematical_logic

   Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.

4. Foundations of mathematics - Wikipedia

   en.wikipedia.org/wiki/Foundations_of_mathematics

   The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, parts of computer science. Subsequent discoveries in the 20th century then stabilized the foundations of ...

5. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

6. Class (set theory) - Wikipedia

   en.wikipedia.org/wiki/Class_(set_theory)

   In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.

7. Zermelo–Fraenkel set theory - Wikipedia

   en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

   Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for "choice", [1] and ZF refers to the ...

8. Algebra of sets - Wikipedia

   en.wikipedia.org/wiki/Algebra_of_sets

   It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.

9. Theory (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Theory_(mathematical_logic)

   In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language.In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory.