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1. Model existence theorem. We fix a first order logic F such that
 

Summary: 1. Model existence theorem.
We fix a first order logic F such that
C = .
We let S be the set of statements of F and we suppose
S.
We let
VFT
be the set of variable free terms. For each s VFT we let
[s] = {t VFT : (s = t)}.
We have proved that
(i) s [s];
(ii) s [t] if t [s];
(iii) s [u] if t [s] and u [t].
That is, {(s, t) VFT : t [s]} is an equivalence relation on bfV FT} and {[s] :
s VFT} is the set of equivalence classes.
We let
D = {[s] : s VFT}.
We define
C : C D
by letting C)(c) = [c] for c C.

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics