In the 2nd paragraph at Kolmogorov complexity, these is the following sentence.
"In particular, for almost each object it is not possible to compute even a lower bound for its Kolmogorov complexity ..."
Does for almost each object have a particular mathematical meaning. Am I missing something, this does not appear to me, to be good English grammar, in the context where it is used?
I think you are right about the grammar. The appropriate mathematical phrase would be "for almost every object" or even better, "almost all objects". So I suggest you edit the wikipedia page to make the change..
"Almost all" has a precise meaning you don't need to know to get the grammar right. For example, almost all real numbers are irrational.
Edit: Noting the comment from @dbx , I wonder whether it's worth fixing grammar on a page that seems to need a lot more fixing.