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...

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

Scott–Potter set theory Constructive set theory Zermelo set theory General set theory Non-well-founded set theory List of first-order theories § Set theories Holmes...

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

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

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...

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