1.
T :
1) L T.
:
(D3) (jÙy) Ø(jØy).
(D4) (jÚy) (Øjy).
(D5) (jy) ((jy)Ù(yj)).
(D6) ($a)j Ø("a)Øj.
2) .
3) .
.
:
(AS -1) j(yj) .
(AS -2) (j(yc))((jy)(jc)) .
(AS -3) (ØjØy)((Øjy)j) .
(AS -4) ("a)(jy)(j("a)y) , aÏ Free j.
(AS -5) ("a)jj¢ , j t a j¢ = j .
a- j.
:
(R 1) = (MP) ( ): j jy y.
(R 2) = (Gen) = (G) ( ): j ("a)j.
() . . T⊢j.
1. 1. () .
2. () .
3. (MP) T⊢j T⊢jy, T⊢y.
4. (Gen) T⊢j, T⊢ ("a)j a.
2. 1. ⊢j ⊢y, ⊢jÚy.
2. ⊢Øj, ⊢jy y.
3. ⊢y, ⊢jy j.
4. ⊢j ⊢y, ⊢jÙy .
5. (S) ⊢jy ⊢yc, ⊢jc.
3. 1. ⊢jy aÏ Free j, ⊢j("a)y.
, ⊢jÚy aÏ Free j, ⊢jÚ("a)y.
2. ⊢jy aÏ Free y, ⊢ ($a)jÚy.
4. 1. j¢ a- j ⊢j, ⊢j¢.
2. (GnG) ⊢j , ⊢ ("a)j.
5. j¢ a- j, ⊢j¢($a)j.
2.
I.
1. -
T T ¢ = T +{j} , T j T, j L T. y L T T ¢ y , j, T⊢jy.
, .
. . j = (x = 1) T¢ = Ar +{j}, T⊢ (" x)(x = 1). Ar ⊢ (x = 1)(" x)(x = 1), Ar ⊢ ($ x)(x = 1)(" x)(x = 1), Ar ⊨ ($ x)(x = 1)(" x)(x = 1).
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II.
2. ⊢jy ⊢ ($a)j, aÏ Free y, ⊢y.
III.
3. 1. ⊢Øjy ⊢ØjØy, ⊢j.
2. ⊢ØjyÙØy, ⊢j.
IV.
4. 1. ⊢jc ⊢yc, ⊢jÚyc.
,
2. ⊢jc, ⊢yc,⊢jÚy, ⊢c.
3. ⊢jc, ⊢Øjc, ⊢c.
3.
T, T , T . T ⊨j.
1.
T ⊢j, T ⊨j.
.
2. .
3. .
4. ø
, .
5. ø
T . T ⊢j T ⊨j.
. j T T ⊢j, T ¢ = T +{Øj} .
.
6. ( ).
.
u: p i Xi. u : .
1. .. . .: , 1995.
2. . . .: , 1973.
3. .. : - , . 2 2000.
4. .., .., : -. : - , 2011.
5. .. . .: , 1981.
6. .. . . . .: , 1966.