什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
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Formal Sets
A formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.
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: n( U% v6 H. n5 J; K% pThe only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.


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S := { 1 .. 5};
8 J/ {& `) n( n6 d! _5 H. P, l> P := PowerSet(S);
P;
6 w9 e  n8 F  I, wPFS:=PowerFormalSet(S);
* w) d$ m2 [( U, ~1 f$ S- ^PFS;
F := { 2, 4 };
FF := { 2/3, 4 };

7 N# O9 N$ n3 A- L) S5 D7 E F in P;
FF in P;
! A# ~9 M* N: h. k  N) v F in PFS;
* @, d; I6 z+ n, E  H  N/ t1 jFF in PFS;
4 j* ^$ v: \5 d7 x1 x- OSet of subsets of { 1 .. 5 }
' {3 {" h$ {1 m. R  c7 _  ^Set of formal subsets of { 1 .. 5 }
; b& x9 }/ r" j/ r4 utrue
false
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>>  F in PFS;
- ?% E9 ]' v  S: ~! k- Z, _      ^
9 R6 t( K, \0 z* J' j7 vRuntime error in 'in': Bad argument types
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, K9 }( a1 {) B% V) r$ W>> FF in PFS;
7 E: f& x1 N  S+ [      ^
& S" ~) \% f( Z7 e* M- RRuntime error in 'in': Bad argument types