The undecidability of the II4 theory for the R. E. wtt and Turing degrees

Journal of Symbolic Logic 60 (4):1118 - 1136 (1995)
We show that the Π 4 -theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters
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