Rosser sentence
E943472
arithmetical sentence
formal sentence
mathematical logic concept
self-referential statement
undecidable sentence
The Rosser sentence is a self-referential statement in mathematical logic, devised by J. Barkley Rosser, that strengthens Gödel’s incompleteness theorem by showing a system’s incompleteness without assuming its consistency.
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
arithmetical sentence
ⓘ
formal sentence ⓘ mathematical logic concept ⓘ self-referential statement ⓘ undecidable sentence ⓘ |
| appearsInWork | Extensions of some theorems of Gödel and Church NERFINISHED ⓘ |
| appliesTo |
any consistent, effectively axiomatized extension of Robinson arithmetic
ⓘ
any consistent, recursively axiomatizable extension of Peano arithmetic ⓘ |
| assumptionWeakenedFrom | ω-consistency ⓘ |
| assumptionWeakenedTo | mere consistency ⓘ |
| avoidsAssumption | ω-consistency of the theory ⓘ |
| comparedTo | Gödel sentence ⓘ |
| constructedIn | 1936 ⓘ |
| definedOver | a theory capable of representing recursive functions ⓘ |
| field |
mathematical logic
ⓘ
metamathematics ⓘ proof theory ⓘ |
| formalizes | statement about its own unprovability in a stronger way ⓘ |
| hasAuthor | J. Barkley Rosser NERFINISHED ⓘ |
| hasConsequence | no consistent, recursively axiomatizable, sufficiently strong theory is complete ⓘ |
| improvesOn | Gödel’s original incompleteness proof ⓘ |
| language | first-order arithmetic ⓘ |
| namedAfter | J. Barkley Rosser NERFINISHED ⓘ |
| namedEntity | true ⓘ |
| property |
neither provable nor refutable in the theory if the theory is consistent
ⓘ
true but unprovable in the theory if the theory is consistent ⓘ |
| relatedTo |
Gödel sentence
ⓘ
Gödel’s incompleteness theorems NERFINISHED ⓘ Peano arithmetic NERFINISHED ⓘ arithmetization of syntax ⓘ consistency ⓘ diagonal lemma ⓘ formal arithmetic ⓘ provability predicate ⓘ recursively axiomatizable theories ⓘ self-reference ⓘ ω-consistency ⓘ |
| requires | effective axiomatizability of the theory ⓘ |
| shows | incompleteness without assuming consistency ⓘ |
| strengthens | first incompleteness theorem NERFINISHED ⓘ |
| topicIn |
advanced logic textbooks
ⓘ
courses on incompleteness theorems ⓘ |
| uses | Rosser trick NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.