什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：

% F( P5 x1 n3 U1 h$ G1 j( iFormal Sets
A formal set consists of the subset of elements of some carrier set (structure) on which a certain predicate assumes the value `true'.
% w% R6 ?' h- m
6 N$ Z5 t% \2 |- ?+ E4 U! \The only set-theoretic operations that can be performed on formal sets are union, intersection, difference and symmetric difference, and element membership testing.



S := { 1 .. 5};
> P := PowerSet(S);
P;
PFS:=PowerFormalSet(S);
PFS;
& C5 f9 S! f. G% N# O4 DF := { 2, 4 };
+ h7 W' Y8 l6 I: E7 M5 Q; NFF := { 2/3, 4 };

6 s. L5 W+ K+ e2 Z F in P;
FF in P;
F in PFS;
FF in PFS;
0 I. }( p, x( v& }0 L& k5 SSet of subsets of { 1 .. 5 }
! u7 R$ _. \, D7 D. ySet of formal subsets of { 1 .. 5 }
2 W7 N( |5 l$ ]true
false

>>  F in PFS;
: q; @5 a3 p1 r9 m! O+ C3 r      ^
! N8 S$ A6 J1 H& l4 W' d1 S. TRuntime error in 'in': Bad argument types


>> FF in PFS;
% e7 Z& Y0 D4 O. v      ^
) i: |5 p& ?$ S  ~1 t- WRuntime error in 'in': Bad argument types