什麽是形式集合Formal Sets/PowerFormalSet？

lilianjie

哪位能给理解下：

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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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};
1 `. \, O0 s0 F# f( L> P := PowerSet(S);
P;
, a, u4 j! L9 S' GPFS:=PowerFormalSet(S);
" w# T* W( Z7 m- K, N! KPFS;
F := { 2, 4 };
FF := { 2/3, 4 };
# f; n0 C" D. e. q  q( m
F in P;
( @  l2 @8 c" S$ X, n& JFF in P;
+ u4 T* G% F* F, ] F in PFS;
6 b) s; U( b# N; `% t, A* qFF in PFS;
Set of subsets of { 1 .. 5 }
0 }, W3 b: v* i' v) `Set of formal subsets of { 1 .. 5 }
true
false

* S  ~# @+ Y( l# W  [>>  F in PFS;
      ^
' \2 p& s; n) d" j" E7 s' Q3 ?Runtime error in 'in': Bad argument types
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& a$ a  j, @2 p, e" w>> FF in PFS;
: M. \+ i$ c6 t% \      ^
Runtime error in 'in': Bad argument types