The Kripke–Platek set theory (KP), pronounced /ˈkrɪpki ˈplɑːtɛk/, is an axiomatic set theory developed by Saul Kripke and Richard Platek. The theory can... 8 KB (1,321 words) - 12:19, 1 January 2024 |
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... 5 KB (664 words) - 21:23, 21 April 2024 |
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... 91 KB (11,505 words) - 23:41, 27 April 2024 |
set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory... 14 KB (2,297 words) - 15:00, 2 April 2024 |
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... 202 KB (33,317 words) - 17:18, 28 April 2024 |
theory Naive set theory S (set theory) Kripke–Platek set theory Scott–Potter set theory Constructive set theory Zermelo set theory General set theory... 1 KB (127 words) - 18:06, 8 February 2024 |
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... 4 KB (648 words) - 07:18, 6 March 2024 |
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... 10 KB (1,506 words) - 08:10, 9 September 2023 |
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... 9 KB (448 words) - 16:05, 3 August 2022 |
Ordinal analysis (category Proof theory) first theory of inductive definitions. KP, Kripke–Platek set theory with the axiom of infinity. CZF, Aczel's constructive Zermelo–Fraenkel set theory. EON... 41 KB (4,022 words) - 09:17, 28 April 2024 |
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... 4 KB (633 words) - 21:31, 22 March 2024 |
Urelement (redirect from Atom (set theory)) 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... 8 KB (995 words) - 17:11, 9 November 2023 |
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... 782 bytes (88 words) - 06:01, 4 March 2024 |
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... 9 KB (1,262 words) - 02:59, 23 February 2024 |
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... 751 bytes (108 words) - 03:20, 24 April 2024 |
politician Richard Platek, Kripke–Platek set theory Robert Platek, Spezia Calcio owner Kripke–Platek set theory Kripke–Platek set theory with urelements... 1,002 bytes (140 words) - 17:29, 22 March 2023 |
Large countable ordinal (category Proof theory) 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... 40 KB (5,320 words) - 22:53, 5 March 2024 |
List of mathematical logic topics (section Set theory) Well-founded set Well-order Power set Russell's paradox Set theory Alternative set theory Axiomatic set theory Kripke–Platek set theory with urelements... 14 KB (1,012 words) - 19:53, 12 November 2023 |
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... 9 KB (1,455 words) - 14:40, 25 January 2024 |
Nonrecursive ordinal (category Proof theory) {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... 12 KB (1,807 words) - 07:56, 18 April 2024 |
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in... 47 KB (6,252 words) - 07:04, 26 April 2024 |
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously... 8 KB (1,180 words) - 15:49, 26 February 2024 |
Mathematical logic (section Set theory and paradoxes) 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... 68 KB (8,329 words) - 22:09, 28 April 2024 |
extensions of Kripke–Platek set theory, Bishop-style systems of constructive mathematics or Martin-Löf-style systems of intuitionistic type theory. Ordinal... 68 KB (12,660 words) - 18:33, 4 April 2024 |
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... 3 KB (365 words) - 13:59, 5 March 2024 |
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... 34 KB (4,715 words) - 07:25, 14 February 2024 |