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Summary: Terms.
We fix a first order language and we let
S
be its set of symbols. (We may have called this the alphabet previously.)
1. GĻodel numbering of symbols.
S is the disjoint union of the sets
Punct, Logical, Const, Var, Func, Pred
where Punct is the set of punctuation symbols
( , )
Logical is the set of logical symbols
Const is the set of constant symbols
ck
where the ks run over a subset of N+
with the property that if 1 j < k and k is
in this set then so is j;
Var is the set of variable symbols
xk, k N+
Func is the set of function symbols
fn
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