Corrigendum: "On the complexity of the successivity relation in computable linear orderings"
Rodney G. Downey, Steffen Lempp, Guohua Wu · Journal of Mathematical Logic · 2017
We indicate how to fix an error in the proof of the Main Theorem of our original paper pointed out to us by Zubkov.The main result of our paper [2] reads as follows:Main Theorem.Let A be an infinite computable linear ordering with infinitely many successivities.Suppose that C is any c.e. set with Succ(A) ≤ T C. Then there is a computable linear ordering B isomorphic to A whose successivity relation has Turing degree deg T (C).Now, Chubb, Frolov and Harizanov [1] had already handled the case of successivities occurring arbitrarily far to the right in a linear order A without right endpoint; and their proof can easily be adapted to the case of any point in A (including the "virtual limit points" +∞ and -∞) being a limit point of successivities; more precisely, their proof can handle the case when, given a fixed a ∈ A ∪ {+∞}, for any b < A a, there are infinitely many successivities in the interval (b, a), and, 1792002-1 J. Math.Log.2017.17.Downloaded from www.worldscientific.comby 23.94.58.