项的值 设σ是Nc在I中的一个指派,如下归纳定义Nc的项t在I中σ 下的值切(简记为t) (1)当t为个体变元符号x1(∈N)时,(x1)=0(x) (2)为t为个体常元符号ck时,(ck)=ck (3)当t为門(t1,t2,……,tm)时,=「m(t,鸪,……,tm) 在例320中,是Nc在1中的如下指派: a(x;)=i(任i∈N) 则:x=0(x;)=i(i∈N) C=0 (1(x1)=f(x)=升(1)=1+1=2∈N (f2(x1,x2)=f2(x,x) (f3(x1,x2)=f(x1,m)=x:吗=3 (1(2(x1,x4))=f1(2(x1,x4)”)=升(f(x,x4) (x1+x4)+1=1+4+1=6 对任任意项t及指派σ,t∈D, % σ NL  I  -CDE NL - t  I  σ  t σ I (" t σ): (1) F t $ xi (i ∈ N ) / (xi) σ I = σ(xi) . (2)  t , ck / (ck) σ I = ck . (3) F t  f m(t1, t2, ··· , tm) / t σ I = f m(t σ 1 , tσ 2 , ··· , tσ m). ! G 3.20  σ NL  I1  - σ(xi) = i (: i ∈ N ) . xσ i = σ(xi) = i(i ∈ N ) cσ = c = 0 (f 1 1 (x1))σ = f 1 1 (xσ 1 ) = f 1 1 (1) = 1 + 1 = 2 ∈ N (f 2 2 (x1, x2))σ = f 2 2 (xσ 1 , xσ 1 ) = xσ 1 + xσ 2 =1+2=3 (f 2 3 (x1, x2))σ = f 3 2 (xσ 1 , xσ 1 ) = xσ 1 · xσ 2 = 3 (f 1 1 (f 2 2 (x1, x4)))σ = f 1 1 ((f 2 2 (x1, x4))σ ) = f 1 1 (f 2 2 (xσ 1 , xσ 4 )) = (xσ 1 + xσ 4 )+1=1+4+1=6 ::/- t H - σ, t σ ∈ D. 3