Is there a generic word for "all of x type of thing"?

Solution 1:

Try the universe of trees, vehicles etc. NB - the term seems particularly apt for describing stars. :)

Solution 2:

I don't believe there's a single word which would apply to every example, every "type of thing," because everything is different.

You might get away with gamut, in certain circumstances.

The complete range or scope of something.
The whole gamut of human emotion

[ODO]

ODO also gives a number of synonyms:

range, spectrum, span, sweep, compass, scope, area, breadth, width, reach, extent, catalogue, scale, sequence, series; variety

Gamut in particular has uses for continuous ranges, such as colour or sound (or emotions). You might use it to refer to the brilliance/magnitude of stars. You could certainly say "the whole gamut of chimneys," and that could mean every chimney or [more likely] every type of chimney.

Another useful word is myriad, an uncountable number. This is often used as a noun, "a myriad of stars" but I prefer its adjectival use:

I searched myriad stars and found nothing.

In my mind, myriad conjures up something shimmering and ill-defined, so it works well for stars or flies or birds, but less well for trees.

However, as Jeffrey Kemp indicates in comments, metaphorical use of a standard collective noun can also be used, probably pluralised as "searched through forests of trees, galaxies of stars" or whatever.

Solution 3:

Would not the word every work in such a case?

• I looked over every tree and could not find a match.
• I looked over every vehicle and could not find a match.
• I looked over every star and could not find a match.

Edit

An alternative to every could possibly be all-encompassing

• I looked over all-encompassing trees and could not find a match.
• I looked over all-encompassing vehicles and could not find a match.
• I looked over all-encompassing stars and could not find a match.