In mathematical logic, Loeb's theorem states that in Peano arithmetic, or any formal system including it, for any formula P, if it is provable that 'if P is provable then P is true' then P is itself provable. It is named after Martin Hugo Loeb, who formulated it in 1955, and connects to Curry's paradox. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementIn Peano arithmetic, or any formal system that includes it, for any formula P, if it is provable that the sentence P is provable implies P is true, then P is itself provable. 1 Connections
Sources
1. Loeb's theorem (Wikipedia)
Wikimedia Foundationlead section, first paragraph
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.
lead section, third paragraph
Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955.
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