К АЛЬТЕРНАТИВНОЙ ТЕОРИИ МНОЖЕСТВ

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  • 35

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    . .

    - . : - , . : - , - .

    . , - .

    - . , - . - .

    .

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    .

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    1.

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    1

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    W N W N

    =

    = . - ( )nW N n- W(N).

    N :

    0 1( ) ,... ( ) ( )n n nV N N V N V P V+= = ,

    1( ) ( )n

    nV N V N

    =

    = , P(A) A. ,

    ( ) ( )n nW N V N ( n N ), ( ) ( )W N V N . F N.

    ( ),A V N *A A F.

    1* ( ) * ( ),n

    nW N W N

    =

    = 1

    * ( ) * ( ).nn

    V N V N

    =

    = *N -

    (* ).V N , [4], j * ( )V N (* ).V N *W(N) .

    , * ( )V N - j . * ( )V N j-. , j - - F - - .

    , :* ( ) * ( ),* ( ) * ( ).n nV N W N V N W N

    2. , ,

    U(N) - * ( ).W N

    *W(N) -, U(N) . , - , .

  • 36

    . N . -

    [0, ] { | 0 }.n N n =

    W(N) ([0, ] ( )).v N W N : * ([0, ] * ( )v N W N , [0, ] { * | 0 }.n N n = , [0, ] .

    A B , - : ,f A B (* )f V N . - , , * ( )f V N , . -, , -.

    , N, , -, .

    A *N , A [0, ].

    -.

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    ,( ) ( )k sA W N N f W N

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    - .

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    , - [0, ] A - f, , A - .

    - r, - - .

    , -, .

    [0, ],* \N N , *N -

    [6]. , *N . -

    (0,1) [0, ]: ( ) [ ],f r r= (0,1),r [x] x.

    1 2r r< ,

    2 1 2 1 2 1 2 1( ) ( ) [ ] [ ] 1 ( ) 1.f r f r r r r r r r = =

    , 2 1( ) ( )f r f r . -, 2 1( ) ( ).f r f r , f (0, 1) [0, ]. [0, ] .

    , *N [5], [0, ] *N . , - [0, ] .

    . A .

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    -.

    A (, , -) .

    : , (* )f N A f V N . , ( ) (* ).A f N V N= n ,

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  • 37

    1. . . .: ,1983. 2. Proceedings of the 1st symposium Mathematics in the internal Set Theory. Bratislava, USFR, 1989. 3. Mattes J. Axiomatic approaches to nonstandard analysis. Jahrbuch der Kurt Gdel Geselschaft, 1992. . 61 79. 4. Robinson A. and Zakon E. A set-theoretical characterization of enlargements, in Applications of Model Theory to Algebra, Analysis and prob-ability / W. A. J. Luxemburg (ed.). New York: Holt, Rinehart and Winston, 1969. . 109 122.

    5. Chang S.S. and Keisler H.G. Model theory. North-Holland, Amsterdam, 1990. 6. .. *N // .-. . . , 1994. . 74.

    - , 18 2005 .

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