distinguished element

…“true” ones (called the “distinguished elements” of the set). In the particular case of the system N, one theory T_a is built up on the basis of the language and the set of theorems of N, and another theory T_b is determined by the true sentences of N according…

A Platonist might still ask whether, among all the models of the language of mathematics, there is a distinguished model, which may be considered to be the world of mathematics. Take as the language ℒ₀ pure intuitionistic type theory (see above). It turns…