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The role of true finiteness in the admissible recursively enumerable degrees
2006
Memoirs of the American Mathematical Society
When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of α-finiteness. As examples we discuss both codings of models of
doi:10.1090/memo/0854
fatcat:kxkbxy6jwbavxo5asuffdfgnom