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:
“Here’s the rule for bargains: “Do other men, for they would do you.” That’s the true business precept.”
—Charles Dickens (1812–1870)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)