Constructive set theory information

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...

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...

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

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory, the latter abbreviated as MLTT) is a type theory and an alternative...

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...

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

AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put...

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

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...

Manchester. He is known for his work in non-well-founded set theory, constructive set theory, and Frege structures. Aczel completed his Bachelor of Arts...

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

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

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

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

techniques from recursion theory as well as proof theory. Functional interpretations are interpretations of non-constructive theories in functional ones. Functional...