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.
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References
Brattka, V., Gherardi, G.: Weihrauch degrees, omniscience principles and weak computability (2009), http://arxive.org/abs0905.4679
Brattka, V., Gherardi, G.: Effective choice and boundedness principles in computable analysis (2009), http://arxive.org/abs0905.4685
Ershov, Y.L.: Definability and Computability. Plenum, New-York (1996)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Ershov, Y.L., Lavrov, T.A., Taimanov, A.D., Taitslin, M.A.: Elementary theories. Uspechi Mat. Nauk 20(4), 37–108 (1965) (in Russian)
Hertling, P.: Topologische Komplexitätsgrade von Funktionen mit endlichem Bild. In: Informatik-Berichte, vol. 152, Fernuniversität Hagen (1993)
Hertling, P.: Unstetigkeitsgrade von Funktionen in der effektiven Analysis, Informatik Berichte 208-11/1996, Fernuniversität Hagen (1996)
Hertling, P., Weihrauch, K.: Levels of degeneracy and exact lowercomplexity bounds for geometric algorithms. In: Proc. of the 6th Canadian Conf. on Computational Geometry Saskatoon, pp. 237–242 (1994)
Kechris, A.S.: Classical Descriptive Set Theory. Springer, New York (1994)
Kruskal, J.B.: The theory of well-quasi-ordering: a frequently discovered concept. J. Combinatorics Theory (A) 13, 297–305 (1972)
Kudinov, O.V., Selivanov, V.L.: Undecidability in the homomorphic quasiorder of finite labeled forests. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds.) CiE 2006. LNCS, vol. 3988, pp. 289–296. Springer, Heidelberg (2006)
Kudinov, O.V., Selivanov, V.L.: Undecidability in the homomorphic quasiorder of finite labelled forests. Journal of Logic and Computation 17, 1135–1151 (2007)
Kosub, S., Wagner, K.: The Boolean hierarchy of NP-partitions. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 157–168. Springer, Heidelberg (2000)
Lehtonen, E.: Labeled posets are universal. European J. Combin. 29, 493–506 (2008)
Selivanov, V.L.: Boolean hierarchy of partitions over reducible bases. Algebra and Logic 43(1), 44–61 (2004)
Selivanov, V.L.: Hierarchies of \({\mathbf\Delta}^0_2\)-measurable k-partitions. Math. Logic Quarterly 53, 446–461 (2007)
Selivanov, V.L.: Undecidability in Some Structures Related to Computation Theory. Journal of Logic and Computation 19(1), 177–197 (2009)
Weihrauch, K.: The degrees of discontinuity of some translators between representations of the real numbers. Technical Report TR-92-050, International Computer Science Institute, Berkeley (1992)
Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)
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Kudinov, O.V., Selivanov, V.L., Zhukov, A.V. (2010). Undecidability in Weihrauch Degrees. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_29
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DOI: https://doi.org/10.1007/978-3-642-13962-8_29
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