Nov 26, 2012

Hilbert's Program 3_Documented by Marsigit



Hilbert's Program 3


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   
    branch.
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
axioms.
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.


1 comment:

  1. Syahrial
    16701251015
    S2 PEP kelas B 2016
    3 program Hilbert’s diatas memberikan pelajaran kepada kita semua. Agak sedikit sulit bagi saya dalam memahami hal di atas namun dapat saya pahami seperti yang diungkapkan diatas adalah bahwa aksioma harus benar-benar memberikan sistem formal untuk cabang yang diinginkan matematika. Ada dua hal yang harus dibuktikan menyiratkan kecukupan yaitu tingkat Kesehatan dan Kelengkapan.

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