弱本质不可判定理论的可互解释性
Mutual Interpretability of Weak Essentially Undecidable Theories
摘要：
Kristiansen和Murwanashyaka最近证明了Robinson算术Q在满二叉树的基本理论T中是可解释的。我们证明，相反，T是可解释的Q通过产生一个正式的解释T在一个基本的级联理论，从而也建立相互解释的T与几个著名的弱本质上不可判定的理论的号码，字符串和集合。我们还介绍了一个“混合”的基本理论的字符串和树，并建立其相互解释与罗宾逊的弱算术R，弱理论的二叉树WT的Kristiansen和Murwanashyaka和弱级联理论的Higuchi和Hirohata。
英文摘要：
Kristiansen and Murwanashyaka recently proved that Robinson arithmetic Q is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings and sets. We also in introduce a "hybrid" elementary theory of strings and trees and establish its mutual interpretability with Robinson's weak arithmetic R, the weak theory of binary trees WT of Kristiansen and Murwanashyaka and a weak concatenation theory of Higuchi and Hirohata.
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