Abstract class field theory (a finitary approach)

A definition of the reciprocity homomorphism in Neukirch's abstract class field theory is given. This definition uses fairly large additional non-ramified extensions, but they are all finite. This will enable one to apply the theory thus constructed to the effectivization (algorithmization) of local and global class field theory alike.
The combination of Neukirch's and Hazewinkel's approaches used in the paper clarifies class field theory even at the abstract level of exposition.