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:
“It’s the misfortune of German authors that not a single one of them dares to expose his true character. Everyone thinks that he has to be better than he is.”
—Franz Grillparzer (1791–1872)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)