@fast,
I still haven't seen any satisfactory justification for the claim that mathematical objects exist but fictional objects dont. Apart from the circularities and special pleading pointed out so far, I think there are intractable problems with the realist position as expressed on this thread.
I assume that in order for some thing to have some property, then that property must exist, but the properties of mathematical objects are themselves abstract objects. So the only properties that, for example, numbers, could have, that confer existence, would need to be non-mathematical. I'll assume that three exists because I have three books on my computer. But I'm told that Lincoln doesn't exist, and Lincoln is a member of the set of all US presidents, a set whose only property is the inclusion of presidents. So, either that class doesn't exist or Lincoln does exist.
Anyway, as this is the severalth time we've had this discussion and there doesn't appear to be much chance that the objections will be met, I've pretty much had enough too. For those such as Zetherin, who think that this matter is somehow settled, be aware that there are plenty of philosophers who reject realism about abstract objects, Benacerraf and Field being prominent examples, and there are those who hold that fictional and imaginary objects are on an equal footing with mathematical objects, that all qualify as abstract objects, Zalta has done a lot to rigourise this position. Then there's Balaguer, who agrees with Egregias, that there's no truth either way. Articles by all of these, except Benacerraf, can be accessed through Chalmers site.