Gödel's incompleteness theorems
GPTKB entity
Statements (65)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
formal systems
|
| gptkbp:consists_of |
two theorems
|
| gptkbp:has_applications_in |
gptkb:computer_science
|
| gptkbp:has_implications_for |
philosophy of mathematics
|
| gptkbp:has_influenced |
computer programming languages
|
| gptkbp:has_produced |
extensive research
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's incompleteness theorems
|
| gptkbp:influenced_by |
Hilbert's program
|
| gptkbp:is_a |
gptkb:software_framework
theorem in mathematical logic result in mathematical logic theorem about provability foundational result result of Gödel's work theorem in the philosophy of mathematics theorem that challenges completeness theorem that has been proven theorem that has historical significance theorem that has practical implications theorem that has theoretical implications theorem with philosophical implications |
| gptkbp:is_associated_with |
gptkb:Gödel_numbering
|
| gptkbp:is_cited_in |
academic papers
philosophers of mathematics many mathematicians |
| gptkbp:is_considered |
a cornerstone of modern mathematics
a major result in mathematics |
| gptkbp:is_described_as |
textbooks on logic
|
| gptkbp:is_discussed_in |
gptkb:philosophical_debates
gptkb:Gödel's_original_paper gptkb:philosophy mathematical journals conferences on logic |
| gptkbp:is_explored_in |
advanced mathematics courses
mathematical philosophy logic seminars |
| gptkbp:is_fundamental_to |
theoretical computer science
computability theory |
| gptkbp:is_often_seen_in |
by the general public
|
| gptkbp:is_opposed_by |
completeness theorem
|
| gptkbp:is_part_of |
mathematical logic curriculum
|
| gptkbp:is_related_to |
gptkb:Set
formal languages mathematical proofs self-reference Turing's work |
| gptkbp:is_used_in |
proof theory
|
| gptkbp:proposed_by |
gptkb:Kurt_Gödel
|
| gptkbp:published_in |
1931
|
| gptkbp:related_to |
mathematical logic
|
| gptkbp:state |
not all true statements are provable
|
| gptkbp:was_a_demonstration_of |
limitations of formal systems
|
| gptkbp:bfsParent |
gptkb:universal_machine
gptkb:Halting_Problem gptkb:Entscheidungsproblem gptkb:Hilbert's_Entscheidungsproblem gptkb:Principia_Mathematica gptkb:Algorithmic_Information_Theory gptkb:The_Emperor's_New_Mind:_Concerning_Computers,_Minds,_and_the_Laws_of_Physics gptkb:Kurt_Gödel gptkb:The_Emperor's_New_Mind gptkb:the_Principia_Mathematica gptkb:Church-Turing_Thesis |
| gptkbp:bfsLayer |
5
|