True Arithmetic

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:

    This is the true joy in life, the being used for a purpose recognized by yourself as a mighty one; the being thoroughly worn out before you are thrown on the scrap heap; the being a force of Nature instead of a feverish selfish little clod of ailments and grievances complaining that the world will not devote itself to making you happy. And also the only real tragedy in life is being used by personally minded men for purposes which you recognize to be base.
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    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.
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