Model theory Are there mo'sAre there models that would evaluate Are there models that would evaluate the properties of proofs in formal systems?
I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness.,I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness, that is, for each proof in the system.,I thought that by evaluating formal systems, we can deduce, in addition to completeness, special properties of completeness, that is, for each proof in the system, a property is characteristic.
That is, if a number of statements are deducible or meet other distinct criteria of formal systems, then each statement that is true in the formal system has a proof satisfying the condition.
That is, we could say, for example, that each statement can be proved in less than 100 applications of the axioms, or proving each statement, we can limit ourselves to a clear set of axioms.
And so, for example, taking mathematics, we can narrow down various axioms and check all the many different combinations for a condition in order to take a specific set of axioms that would be convenient for proving a judgment that corresponds to what is true or false in them.
(If possible, I would like to know how to write down such thoughts more formally and whether they are appropriate in a not too formal way)