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Degrees of categoricity of trees and the isomorphism problem
Mathematical Logic Quarterly ( IF 0.4 ) Pub Date : 2019-10-13 , DOI: 10.1002/malq.201700049
Mohammad Assem Mahmoud 1
Affiliation  

In this paper, we show that for any computable ordinal α, there exists a computable tree of rank α + 1 with strong degree of categoricity 0 ( 2 α ) if α is finite, and with strong degree of categoricity 0 ( 2 α + 1 ) if α is infinite. In fact, these are the greatest possible degrees of categoricity for such trees. For a computable limit ordinal α, we show that there is a computable tree of rank α with strong degree of categoricity 0 ( α ) (which equals 0 ( 2 α ) ). It follows from our proofs that, for every computable ordinal α > 0 , the isomorphism problem for trees of rank α is Π 2 α 0 ‐complete.

中文翻译:

树的分类度和同构问题

在本文中,我们表明对于任何可计算的序数α,都存在可计算的等级树 α + 1个 具有高度的分类性 0 2 α 如果α是有限的并且具有强烈的分类性 0 2 α + 1个 如果α是无限的。实际上,这些是此类树的最大可能分类度。对于可计算的极限序数α,我们表明存在一类具有高度分类性的可计算树 0 α (等于 0 2 α )。根据我们的证明,对于每个可计算序数 α > 0 ,等级为α的树的同构问题是 Π 2 α 0 -完成。
更新日期:2019-10-13
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