About: Constructible universe

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Constructible universe Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular class of sets that can be described entirely in terms of simpler sets. L is the union of the constructible hierarchy Lα . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems

Attributes	Values
rdf:type	Thing
rdfs:label	Constructible universe (en)
rdfs:comment	In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular class of sets that can be described entirely in terms of simpler sets. L is the union of the constructible hierarchy Lα . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems (en)
differentFrom	Gödel metric
sameAs	Constructible universe Constructible universe
dbp:wikiPageUsesTemplate	dbt:= dbt:Block_indent dbt:Cite_book dbt:Cite_journal dbt:Distinguish dbt:Math dbt:Mvar dbt:Space dbt:Sub dbt:Sup dbt:Tmath dbt:Var dbt:Set_theory
Subject	Works by Kurt Gödel Constructible universe
Link from a Wikipage to an external page	http://press.princeton.edu/titles/1034.html%7Cisbn=978-0-691-07927-1 https://archive.org/details/admissiblesetsst00barw_0
gold:hypernym	Class
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Constructible_universe?oldid=1074189427&ns=0
Wikipage page ID	343335 (xsd:integer)
page length (characters) of wiki page	31551 (xsd:nonNegativeInteger)
Wikipage revision ID	1074189427 (xsd:integer)
Link from a Wikipage to another Wikipage	Formal language Mahlo cardinal Nonrecursive ordinal Ronald Jensen Well-formed formula Well-founded relation Arithmetical hierarchy Axiom Axiom of choice Axiom of constructibility Axiom of empty set Axiom of extensionality Axiom of global choice Axiom of infinity Axiom of pairing Axiom of power set Axiom of regularity Axiom of union Axiom schema of replacement Axiom schema of specification Bijection Von Neumann cardinal assignment Von Neumann universe Bounded quantifier Works by Kurt Gödel Kurt Gödel Power set Quantifier (logic) Set (mathematics) Set theory Zermelo–Fraenkel set theory Zero sharp Class (set theory) Hyperarithmetical theory List of large cardinal properties Truth value Club set Consistency Continuum hypothesis Hereditarily countable set Hereditarily finite set Minimal model (set theory) Mostowski collapse lemma Ordinal definable set Ordinal number Parameter Elementary equivalence Equinumerosity Inaccessible cardinal Indiscernibles Descriptive set theory Gödel numbering Gödel operation Inner model L(R) Transfinite induction Transitive set Constructible universe Successor ordinal Large cardinal Lexicographic order Limit cardinal Limit ordinal Lévy hierarchy Löwenheim–Skolem theorem Mathematics Measurable cardinal Reflection principle Regular cardinal
has abstract	In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular class of sets that can be described entirely in terms of simpler sets. L is the union of the constructible hierarchy Lα . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Constructible_universe
is differentFrom of	Gödel metric

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 922 MB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software