more from Robert S. Wolf

Single Idea 13519

[catalogued under 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models]

Full Idea

Model theory uses set theory to show that the theorem-proving power of the usual methods of deduction in mathematics corresponds perfectly to what must be true in actual mathematical structures.

Gist of Idea

Model theory uses sets to show that mathematical deduction fits mathematical truth


Robert S. Wolf (A Tour through Mathematical Logic [2005], Pref)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.-8

A Reaction

That more or less says that model theory demonstrates the 'soundness' of mathematics (though normal arithmetic is famously not 'complete'). Of course, he says they 'correspond' to the truths, rather than entailing them.