 
Summary: 1. Trees; context free grammars.
1.1. Trees.
Definition 1.1. By a tree we mean an ordered triple
T = (N, , p)
such that
(i) N is a finite set;
(ii) N;
(iii) p : N {} N;
(iv) if n N+
and dmn pn
then pn
() = .
One can relax the condition that N be finite but we will have no use for infinite
trees.
Suppose Ti = (Ni, i, pi), i = 1, 2 are trees and : N1 N2. We say is an
isomorphism from T1 to T2 if is univalent, rng = N2,
(1) = 2 and p2(()) = (p1()) for N1 {1}.
1.2. Suppose (N, , p) is a tree.
Proposition 1.1. Suppose N. Then there is n N such that dmn pn
.
