什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：
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Formal Sets
# x$ N: w# B- i; HA formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

' g1 ?# e, M; O. cThe 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};
> P := PowerSet(S);
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PFS:=PowerFormalSet(S);
PFS;
F := { 2, 4 };
; J: @. l4 l0 N0 i7 JFF := { 2/3, 4 };

F in P;
FF in P;
F in PFS;
FF in PFS;
Set of subsets of { 1 .. 5 }
, ^) e% H6 K8 ]: `* u) S8 o5 _  eSet of formal subsets of { 1 .. 5 }
true
false
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& ^( m% A* m+ a$ q>>  F in PFS;
0 e7 t6 w% K1 k* \# z5 P      ^
; \8 A; U3 Q( _, X4 O' e' M9 aRuntime error in 'in': Bad argument types

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>> FF in PFS;
* m& ~% d9 B6 t      ^
3 w  s& ~: T& |  v/ lRuntime error in 'in': Bad argument types