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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Rosser sentence canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T11736265 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Rosser sentence Context triple: [Barkley Rosser, notableWork, Rosser sentence]
-
A.
Löb's theorem
Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
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B.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
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C.
Tarski–Mostowski–Robinson theorem
The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
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D.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
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E.
Ramsey sentence
A Ramsey sentence is a logical reformulation of a scientific theory that replaces its theoretical terms with existentially quantified variables to capture only its structural content.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Rosser sentence Target entity description: 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.
-
A.
Löb's theorem
Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
-
B.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
-
C.
Tarski–Mostowski–Robinson theorem
The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
-
D.
Gentzen’s consistency proof for arithmetic
Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
-
E.
Ramsey sentence
A Ramsey sentence is a logical reformulation of a scientific theory that replaces its theoretical terms with existentially quantified variables to capture only its structural content.
- F. None of above. chosen
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 ⓘ |
| 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 ⓘ |
| hasConsequence | no consistent, recursively axiomatizable, sufficiently strong theory is complete ⓘ |
| improvesOn | Gödel’s original incompleteness proof ⓘ |
| language | first-order arithmetic ⓘ |
| namedAfter | J. Barkley Rosser ⓘ |
| 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 ⓘ
linked to:
Gödel's incompleteness theorems
Peano arithmetic ⓘ 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
ⓘ
linked to:
Gödel's incompleteness theorems
|
| topicIn |
advanced logic textbooks
ⓘ
courses on incompleteness theorems ⓘ |
| uses | Rosser trick ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Rosser sentence Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.