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These results from a part of the author's doctoral thesis, Cornell University, 1992. The author wishes to thank his thesis advisor Prof. Richard Shore for his overall advice
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Yang, Y. Iterated trees and fragments of arithmetic. Arch Math Logic 34, 97–112 (1995). https://doi.org/10.1007/BF01270390
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DOI: https://doi.org/10.1007/BF01270390