Metalogical theories
Logic and Metalogic

Demonstration theory, also known as proof theory, is a branch of mathematical logic founded by the German mathematician D. Hilbert. Hilbert at the beginning of the 20th century, with the aim of demonstrating the coherence of mathematics. This objective was invalidated by the famous incompleteness theorem of the Austrian mathematician and logician K. Gödel (1931). Demonstration theory nevertheless developed, thanks in particular to the work of mathematicians and logicians J. Herbrand (1909-1945) and G. Gentzen (1908-1931)....