科研之友
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摘要
Assuming that 0(#) exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure A such that Sp(A) = {x' : x is an element of Sp(A)}, where Sp(A) is the set of Turing degrees which compute a copy of A. More interesting than the result itself is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full nth-order arithmetic for all n, cannot prove the existence of such a structure.
- 出版日期2013-6
