The Kierstead's conjecture and limitwise monotonic functions
A linear order is \(\Pi_1^0\)-rigid if it does not have any nontrivial \(\Pi_1^0\)-automorphism. Let \(\zeta, \eta\) are the order types integers and rational numbers, respectively. \textit{H. A. Kierstead} [J. Symb. Log. 52, 681--688 (1987; Zbl 0637.03043)] conjectured that every computable copy of a linear order \(\mathcal L\) has a strongly nontrivial \(\Pi_1^0\)-automorphism if and only if \(\mathcal L\) contains an interval of order type \(\eta\). In the paper under review, the authors prove this conjecture for linear orders whose order types are \(\Sigma_{q\in Q}F(q)\), where \(F\) is an extended \(\emptyset'\)-limitwise monotonic function, i.e. \(F\) can take the value \(\zeta\).
scientific article; zbMATH DE number 6856630
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