Zermelo-Fraenkel set theory with the Axiom of Choice
GPTKB entity
Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:collection
|
| gptkbp:bfsLayer |
9
|
| gptkbp:bfsParent |
gptkb:Continuum_Hypothesis
|
| gptkbp:applies_to |
gptkb:Mathematician
gptkb:television_channel gptkb:Research_Institute geometry statistics mathematical logic probability theory |
| gptkbp:based_on |
axioms
|
| gptkbp:developed_by |
gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel |
| https://www.w3.org/2000/01/rdf-schema#label |
Zermelo-Fraenkel set theory with the Axiom of Choice
|
| gptkbp:includes |
Axiom of Extensionality
Axiom of Pairing Axiom of Union Axiom of Choice Axiom of Infinity Axiom of Power Set Axiom of Replacement |
| gptkbp:ingredients |
first-order logic
|
| gptkbp:is_a |
gptkb:software_framework
axiomatic set theory axiomatic system formal system theoretical foundation |
| gptkbp:is_compared_to |
ZFC
|
| gptkbp:is_criticized_for |
continuum hypothesis
constructivists non-constructive proofs paradoxes in set theory incompleteness results intuitionists axiomatic assumptions existence of non-measurable sets independence of the Axiom of Choice |
| gptkbp:is_related_to |
gptkb:Zorn's_lemma
Cantor's theorem cardinal numbers transfinite numbers axiomatic systems ordinal numbers mathematical induction Zermelo's well-ordering theorem set-theoretic topology set-theoretic foundations well-ordering principle |
| gptkbp:is_studied_in |
set theory courses
|
| gptkbp:is_used_in |
gptkb:philosopher
gptkb:computer_science gptkb:Mathematician philosophy of mathematics foundations of mathematics |
| gptkbp:provides |
foundation for mathematics
|