Gödel's first incompleteness theorem
GPTKB entity
Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:has_impact_on |
mathematical logic
philosophy of mathematics |
| gptkbp:historical_significance |
in the development of logic
in the philosophy of mathematics |
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's first incompleteness theorem
|
| gptkbp:is_a |
theorem in mathematical logic
theorem about provability theorem that challenges completeness theorem with philosophical implications result of mathematical logic theorem about axiomatic systems theorem about formal languages theorem about formal systems theorem about truth theorem with mathematical implications |
| gptkbp:is_cited_in |
research articles
academic papers many works in mathematical logic |
| gptkbp:is_considered_as |
a fundamental result in mathematical logic
|
| gptkbp:is_described_as |
textbooks on mathematical logic
philosophy of mathematics literature |
| gptkbp:is_discussed_in |
gptkb:philosophical_debates
gptkb:Gödel's_original_paper |
| gptkbp:is_explored_in |
mathematical research
computer science research |
| gptkbp:is_influenced_by |
Hilbert's program
|
| gptkbp:is_opposed_by |
gptkb:Hilbert's_completeness_theorem
|
| gptkbp:is_part_of |
gptkb:Gödel's_incompleteness_theorems
|
| gptkbp:is_related_to |
gptkb:Gödel's_second_incompleteness_theorem
gptkb:Gödel_numbering consistency arithmetic self-reference formal systems |
| gptkbp:is_used_in |
computability theory
proof theory |
| gptkbp:proposed_by |
gptkb:Kurt_Gödel
|
| gptkbp:published_by |
1931
|
| gptkbp:state |
In any consistent formal system that is capable of expressing arithmetic, there are true statements that cannot be proven within the system.
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| gptkbp:bfsParent |
gptkb:Kurt_Gödel
|
| gptkbp:bfsLayer |
4
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