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Löb's theorem

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) is the assertion that the formula P is provable in PA, we may express this more formally as

Modal proof of Löb's theorem, Löb's theorem in provability logic & Examples

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Löb's theorem in provability logic

Modal proof of Löb's theorem

Examples

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Löb's theorem

Nodes24
Edges23
Triples30
Avg. degree1.92
Density0.083333
Components1

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Löb's theorem

Top relations

related to External links · 10
Löb's theorem → December, Löb's, March, Philosophy, PlanetMath, Provability Logic, Retrieved, Rineke, Stanford Encyclopedia, Verbrugge
related to Examples · 7
Löb's theorem → An, Given, If, Löb's, PA, Ramsey, The
related to Löb's theorem in provability logic · 6
Löb's theorem → Box, Gödel's, Löb's, Provability, That, Then
related to Converse: Löb's theorem implies the existence of modal fixed points · 5
Löb's theorem → Box, Löb's, Not, Thus, When Löb's
related to Modal proof of Löb's theorem · 2
Löb's theorem → K4, Löb's

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displaystyle box theorem vdash rightarrow pa logic löb's provable psi modal formula provability fixed existence points neg true rule 10

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SubjectPredicateObjectConfidenceSrc
Löb's theoremrelated to Converse: Löb's theorem implies the existence of modal fixed pointsNot0.60section
Löb's theoremrelated to Converse: Löb's theorem implies the existence of modal fixed pointsLöb's0.60section
Löb's theoremrelated to Converse: Löb's theorem implies the existence of modal fixed pointsWhen Löb's0.60section
Löb's theoremrelated to Converse: Löb's theorem implies the existence of modal fixed pointsThus0.60section
Löb's theoremrelated to Converse: Löb's theorem implies the existence of modal fixed pointsBox0.60section
Löb's theoremrelated to ExamplesAn0.60section
Löb's theoremrelated to ExamplesLöb's0.60section
Löb's theoremrelated to ExamplesPA0.60section
Löb's theoremrelated to ExamplesGiven0.60section
Löb's theoremrelated to ExamplesIf0.60section
Löb's theoremrelated to ExamplesRamsey0.60section
Löb's theoremrelated to ExamplesThe0.60section

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