Undecidability in Weihrauch degrees

Authors:
Oleg V. Kudinov;Victor L. Selivanov;Anton V. Zhukov
Affiliations:
S.L. Sobolev Institute of Mathematics, Novosibirsk, Russia;A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia;Novosibirsk State Pedagogical University, Novosibirsk, Russia
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

We prove that the 1-quasiorder and the 2-quasiorder of finite k-labeled forests and trees have hereditarily undecidable first-order theories for k ≥ 3. Together with an earlier result of P. Hertling, this implies some undecidability results for Weihrauch degrees.