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...

related to topos theory. It is also used in the study of absoluteness, and there part of the formulation of Kripke-Platek set theory. The restriction...

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...

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...

Internal set theory Pocket set theory Naive set theory S (set theory) Double extension set theory Kripke–Platek set theory Kripke–Platek set theory with urelements...

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

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

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...

of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and...

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...

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...

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...

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

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

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...

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

set theories include: Weak theories lacking powersets: S' (Tarski, Mostowski, and Robinson, 1953); (finitely axiomatizable) Kripke–Platek set theory;...

In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}}...

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...

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...

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...

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

Tarski's semantic theory should be counted either as a correspondence theory or as a deflationary theory. Kripke's theory of truth (Saul Kripke 1975) is based...

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...

non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica...

mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine...

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...

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

hierarchy. This research is related to weaker versions of set theory such as Kripke–Platek set theory and second-order arithmetic. Pointclass Prewellordering...