  The theory of Fermion oscillators has two essential ingredients: zero-point
energy and Pauli exclusion principle. We devlop the theory of the statistical
mechanics of generalized q-deformed Fermion oscillator algebra with inclusion
principle (i.e., without the exclusion principle), which corresponds to
ordinary fermions with Pauli exclusion principle in the classical limit $q \to
1$. Some of the remarkable properties of this theory play a crucial role in the
understanding of the q-deformed Fermions. We show that if we insist on the weak
exclusion principle, then the theory has the expected low temperature limit as
well as the correct classical q-limit.
