True arithmetic is the set Th of all sentences in the language of first-order arithmetic that are true in . This set is, equivalently, the (complete) theory of the structure (see theories associated with a structure).
Read more about True Arithmetic: Arithmetic Indefinability, Computability Properties, Model-theoretic Properties, True Theory of Second-order Arithmetic
Famous quotes containing the words true and/or arithmetic:
“Every need whose true satisfaction is denied leads by necessity to faith.”
—Johann Wolfgang Von Goethe (1749–1832)
“‘Tis no extravagant arithmetic to say, that for every ten jokes,—thou hast got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.”
—Laurence Sterne (1713–1768)