Nov 26, 2012
Hilbert's Program 3_Documented by Marsigit
Hilbert's program was applied in three steps:
1) Formalize the branch of mathematics to get a
formal system, S.
a) Design an appropriate formal language for the
b) axiomatize the theory in that language.
2) Show that the formal system, S, is adequate.
In other words, the axioms must really give a formal system for the desired branch of mathematics. There are two things that must be proven to imply adequacy.
a) Soundness. Every theorem derivable from the
formal system must be true in the branch of
mathematics the formal system implements.
No false consequences may follow from the
b) Completeness. Everything true in a branch of
mathematics must be derivable as a theorem
from the axioms of the formal system.
3) Prove that S is consistent.