  We prove that Donaldson-Thomas type invariants are equal to weighted Euler
characteristics of their moduli spaces. In particular, such invariants depend
only on the scheme structure of the moduli space, not the symmetric obstruction
theory used to define them. We also introduce new invariants generalizing
Donaldson-Thomas type invariants to moduli problems with open moduli space.
These are useful for computing Donaldson-Thomas type invariants over
stratifications.
