I'm trying to understand David Hilbert's intention in creating a mathematics foundation.
Hilbert's program intention to confirm that we can find a finite set of axioms with completeness,consistency and decidability property .
I want to understand it better.
What kind of axioms would the finite set consist of, axioms about arithmetic?
What kind of prepositions we would be able to generate from this finite set by using a logical system ?
Could the prepositions be about anything ( for example, generating a preposition about the shape of earth from this arithmetic axioms ) ?
If you want to understand Hilbert's Programme better, a very good place to start is http://plato.stanford.edu/entries/hilbert-program/
[By the way, it was no part of the program to be looking for finite sets of axioms; it is only required, inter alia, that there is a finitary procedure for deciding what's an axiom.]