什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：

' Z' l" n; J& [* @2 H3 h5 y2 h9 PFormal Sets
A formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

3 I9 I5 V, |' ^! S: Z2 sThe 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);
P;
PFS:=PowerFormalSet(S);
PFS;
7 G5 K- O9 I: Y$ X* j3 lF := { 2, 4 };
8 v5 n3 K$ @; C& u* kFF := { 2/3, 4 };
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' p, m3 f6 N8 w F in P;
FF in P;
3 Z" W( V) }3 ~. B' A5 o* [. s F in PFS;
FF in PFS;
Set of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
true
false
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7 |# h, O& }" O) @# @3 }. q: n>>  F in PFS;
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6 k5 }$ I2 R( i( rRuntime error in 'in': Bad argument types
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>> FF in PFS;
* C% n. y0 w8 f  H1 a7 C3 B      ^
- s3 j4 U$ z4 v7 L# T! XRuntime error in 'in': Bad argument types