In Kleene's "On Notation for Ordinal Numbers", Journal of Symbolic Logic, Volume 2, Number 4, December 1938, he says that a function of natural numbers is taken to be effective if it is Herbrand-Goedel recursive, and then cites a 1934 set of notes by Goedel. Does this mean primitive recursive or general recursive?

It means general recursive. This looks like a good set of notes about it.

http://www.people.cs.uchicago.edu/~soare/History/compute.pdf

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