什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：

Formal Sets
4 W  o" P2 H& VA formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.

The 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};
9 ]9 V+ V9 r2 y$ G0 w: c* a0 G  l> P := PowerSet(S);
P;
PFS:=PowerFormalSet(S);
PFS;
F := { 2, 4 };
" B' {" j  c; W. A: A) v$ vFF := { 2/3, 4 };

F in P;
8 H6 w2 ~7 D/ z" aFF in P;
5 }/ J+ G* }; w. v1 m) A F in PFS;
FF in PFS;
1 |$ t6 T: {) J4 U' y1 jSet of subsets of { 1 .. 5 }
Set of formal subsets of { 1 .. 5 }
true
; F1 ?1 v* `! f0 F' w6 p$ `false

# N' J" i' H; y4 o0 B>>  F in PFS;
      ^
+ ^& X$ r/ \+ R' ]# d8 [+ a. pRuntime error in 'in': Bad argument types
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6 Q, _/ O/ k, H- p) J: p
' r; A8 ^- I8 Z& C% w* G+ J) @" T# a- w>> FF in PFS;
      ^
Runtime error in 'in': Bad argument types