Abstract
Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degres coincides with the one considered in the \(\Delta_2^0\) degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in [7] that there are d.r.e. degrees a, b, c and a 3-r.e. degree x such that a is the infimum of b, c in the d.r.e. degrees, but not in the 3-r.e. degrees, as a < x < b, c. In this paper, we extend Kaddah’s result by showing that such a infima difference occurs densely in the r.e. degrees.
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Liu, J., Wang, S., Wu, G. (2009). Infima of d.r.e. Degrees. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_34
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DOI: https://doi.org/10.1007/978-3-642-03073-4_34
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