Computation of First Cohomology Groups of Finite Covers Original Research Article

We give several applications of standard methods of group cohomology to some problems arising in model theory concerning finite covers. We prove a conjecture of the author that forG-finite, aleph, Hebrew0-categorical structures the kernels of minimal superlinked finite covers have bounded rank. We show that the cohomology groups associated to finite covers of certain structures (amongst them, the primitive, countable, totally categorical structures) have to be finite. From this we deduce that the finite covers of these structures are determined up to finitely many possibilities by their kernels.