Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

Constructivism also includes the study of constructive set theories such as CZF and the study of topos theory. Constructivism is often identified with...

set theories: Morse–Kelley set theory Von Neumann–Bernays–Gödel set theory Tarski–Grothendieck set theory Constructive set theory Internal set theory...

Look up Appendix:Glossary of set theory in Wiktionary, the free dictionary. This is a glossary of set theory. Contents:  Greek !$@ A B C D E F G H I J...

Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One...

theory Naive set theory S (set theory) Kripke–Platek set theory Scott–Potter set theory Constructive set theory Zermelo set theory General set theory...

of constructive theories such as Heyting arithmetic and constructive set theories (Rathjen 2005). The disjunction property is satisfied by a theory if...

In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise...

axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker...

between KP, generalized recursion theory, and the theory of admissible ordinals. KP can be studied as a constructive set theory by dropping the law of excluded...

proofs were essentially constructive. The first non-constructive constructions appeared with Georg Cantor’s theory of infinite sets, and the formal definition...

constructive set theory, where non-classical logic is employed. The situation is different when the principle is formulated in Martin-Löf type theory...

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics...

{\mathbb {N} }^{\mathbb {N} }} , constructive second-order arithmetic, or strong enough topos-, type- or constructive set theories such as C Z F {\displaystyle...

In set theory, the complement of a set A, often denoted by A ∁ {\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements...

type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations...

is not valid in constructive or intuitionistic logic, and so this separate terminology is mostly used in the set theory of constructive mathematics. In...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

_{0}}} has a constructive axiomatization involving these axioms and e.g. Set induction and Replacement. Axiomatically characterizing the theory of hereditarily...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

calculus. BHK interpretation Computability logic Constructive analysis Constructive proof Constructive set theory Curry–Howard correspondence Game semantics...

such, the above proof is not a constructive one. In fact, in a constructive set theory such as intuitionistic set theory I Z F {\displaystyle {\mathsf...

intuitionistic analogue of Boolean algebras. BHK interpretation Constructive analysis Constructive set theory Harrop formula Realizability Troelstra 1973:18 Sørenson...

Cantor's set theory. Modern constructive set theory includes the axiom of infinity from ZFC (or a revised version of this axiom) and the set N of natural...

Consequentia mirabilis – Pattern of reasoning in propositional logic Constructive set theory Diaconescu's theorem Dichotomy – Splitting of a whole into exactly...

several mathematical theories, such as Kripke–Platek set theory (with the axiom of infinity) and the system CZF of constructive set theory. It was introduced...

"Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University Suppes, Patrick (1972) [1960], Axiomatic Set Theory,...

Cantor considered the set T of all infinite sequences of binary digits (i.e. each digit is zero or one). He begins with a constructive proof of the following...