The Kripke–Platek set theory (KP), pronounced /ˈkrɪpki ˈplɑːtɛk/, is an axiomatic set theory developed by Saul Kripke and Richard Platek. The theory can...

The Kripke–Platek set theory with urelements (KPU) is an axiom system for set theory with urelements, based on the traditional (urelement-free) Kripke–Platek...

cardinals. KP Kripke–Platek set theory Kripke 1.  Saul Kripke 2.  Kripke–Platek set theory consists roughly of the predicative parts of set theory Kuratowski...

Zermelo set theory sufficient for the Peano axioms and finite sets; Kripke–Platek set theory, which omits the axioms of infinity, powerset, and choice, and...

Wittgenstein. His theory of truth. He has also contributed to recursion theory (see admissible ordinal and Kripke–Platek set theory). Two of Kripke's earlier works...

set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory...

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

foundations related to topos theory. See also Kripke-Platek set theory. By a remark in the section on merging sets, a set cannot consistently ruled out...

axiomatic set theory, the axiom of empty set is a statement that asserts the existence of a set with no elements. It is an axiom of Kripke–Platek set theory and...

hierarchy. This research is related to weaker versions of set theory such as Kripke–Platek set theory and second-order arithmetic. This box: view talk edit...

set theory Kripke–Platek set theory with urelements Morse–Kelley set theory Naive set theory New Foundations Pocket set theory Positive set theory S (Boolos...

first theory of inductive definitions. KP, Kripke–Platek set theory with the axiom of infinity. CZF, Aczel's constructive Zermelo–Fraenkel set theory. EON...

include Kripke–Platek set theory with urelements and the variant of Von Neumann–Bernays–Gödel set theory described by Mendelson. In type theory, an object...

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...

set axiom, as in the case of the Kripke–Platek set theory. The power set axiom does not specify what subsets of a set exist, only that there is a set...

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...

Kripke–Platek set theory (Barwise 1975). The smallest example of an admissible set is the set of hereditarily finite sets. Another example is the set...

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...

extension of Kripke–Platek set theory based on an inaccessible cardinal. KPI, an extension of Kripke–Platek set theory based on limits of admissible sets. This...

politician Richard Platek, Kripke–Platek set theory Robert Platek, Spezia Calcio owner Kripke–Platek set theory Kripke–Platek set theory with urelements...

beyond Peano's axioms. For example, the proof-theoretic strength of Kripke–Platek set theory is the Bachmann–Howard ordinal, and, in fact, merely adding to...

Well-founded set Well-order Power set Russell's paradox Set theory Alternative set theory Axiomatic set theory Kripke–Platek set theory with urelements...

admissible ordinal if L α {\displaystyle L_{\alpha }} is a model of Kripke–Platek set theory. In what follows α {\displaystyle \alpha } is considered to be...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

{KPi}}} , an extension of Kripke–Platek set theory stating that each set is contained in a model of Kripke–Platek set theory. Under the condition that...

objects such as the set of all sets at the cost of restrictions on its set-existence axioms. The system of Kripke–Platek set theory is closely related...

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

extensions of Kripke–Platek set theory, Bishop-style systems of constructive mathematics or Martin-Löf-style systems of intuitionistic type theory. Ordinal...

Korea Polytechnic University, South Korea Kripke–Platek set theory with urelements, an axiom system for set theory Kwantlen Polytechnic University, a public...

Kp index, a measure of the global average geomagnetic potential Kripke–Platek set theory, a mathematical axiom system Pentax KP, a 2017 digital SLR camera...