This work is devoted to investigation of complexity of theories
with computable model and
finite number of countable models up to isomorphism
and also possibilities of location of computable model in the spectra
of Ehrefeucht theory.
In the work for all m in omega there are examples of Ehrefeucht
theories of complexity 0^(m) with computable model. Also
there is example of theory with finite number of countable models which
all models are computable but not decidable. And example
of Ehrenfeucht theory which has uncomputable prime and saturated models
but one model of the theory has computable presentation.