Hanf numbers for fragments of ℶh(A)

We describe an ordinalh(A) which plays a key role in the model theory of the admissible fragmentLA. In particular, the Hanf number ofLA is ℶh(A) IfLA isLκ=ω wherecf(k)>ω thenh(A) can be characterized as the least ordinal which is notH(k+)-recursive.

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