A combinatorial method of tackling the problem of hierarchy collapse, and a theorem of Ajtai
نویسنده
چکیده
2. Proposition. For all n ∈ ω there exists a subset B of ω such that E n 6= E n+1. This proposition follows from a theorem of M. Sipser about Boolean circuits (see “Borel Sets and Circuit Complexity”, JACM 1983, pp. 61–69), whose presentation we closely follow. On the way, we study a theorem of Ajtai about the structure of classes of sets of the form E n that uses an analogue of the Borel hierarchy.
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