例3.21 设C={F2} I=<N,{P},,0>是C的一个解释,其中R={<a,a>a∈N} 1,a2, 为D中元素的序列,满足 1=a2 a是Nc在I中的如下指派:0(x1)=a;(任i∈N) 当a为Kc中下列公式时,Ia成立与否? (1)P2(x1,x2 (3)P2(x1,x2)→F2(x2x3); 1)Vx1F2(x1,x2); 解: (1)IF2(x1,x2)当且仅当<,吗>∈当且仅当<a1,a2>∈R 由于a1=a2,故<a,a2>∈R,从而IhP2(x,m2 (2)IbF(x2,x3)当且仅当<吗,>∈P,当且仅当<a,a3>∈R 由于a2≠a3,故< gR,从而I佑P2(x2,x3) (3)IlF2(ax;x2)→P2(x2,x3)当且仅当rP2(x1,a2)或IlF(x2,m3) 但由(1)(2)知:IP2(x1,x2)→F2(x2,x3) (4)Iax1F2(x1,x2) 当且仅当:任意a∈D,I (x1/a 1,T2 当且仅当:任意a∈D,<x(x1/a)(1/)>∈F2 当且仅当:任意a∈D,<a,a2>∈R 但a3∈D,<a3,02>gR.从而IVx1F(x1,x2)! 3.21 % L = {F2 }. I =< N, {R}, ∅, ∅ > L ￾  R = {< a, a > |a ∈ N}. a1, a2, ··· , an, ···  D K2 a0 = a1 = a2 = a3. σ NL  I  - σ(xi) = ai (: i ∈ N ). F α  KL / I | σ α OP(S\ (1) F2(x1, x2); (2) F2(x2, x3); (3) F2(x1, x2)→F2(x2, x3); (4) ∀x1F2(x1, x2); (5) ∀x1∃x2F(x1, x2) . ￾ (1) I | σ F2(x1, x2) FMNF < xσ 1 , xσ 2 >∈ F2 FMNF < a1, a2 >∈ R. 89 a1 = a2, ] < a1, a2 >∈ R, TU I | σ F2(x1, x2). (2) I | σ F2(x2, x3) FMNF < xσ 2 , xσ 3 >∈ F2, FMNF < a2, a3 >∈ R. 89 a2 = a3, ] < a2, a3 >∈ R, TU I | σ / F2(x2, x3). (3) I | σ F2(x1, x2)→F2(x2, x3) FMNF I | σ / F2(x1, x2) ! I | σ F2(x2, x3). ^8 (1)(2) : I | σ / F2(x1, x2)→F2(x2, x3). (4) I | σ ∀x1F2(x1, x2) FMNF:/ a ∈ D, I | σ(x1/a) F2(x1, x2). FMNF:/ a ∈ D, < xσ(x1/a) 1 , x σ(x1/a) 2 >∈ F2. FMNF:/ a ∈ D, < a, a2 >∈ R. ^ a3 ∈ D, < a3, a2 >∈ R. TU I | σ / ∀x1F2(x1, x2). 5