Continuous reducibility : functions versus relations

• Autorzy: Camerlo Riccardo

Identyfikatory

DOI

10.4467/20842589RM.19.002.10650

• Języki publikacji: EN

Abstrakty

EN

It is proved that the Tang-Pequignot reducibility (or reducibility by relatively continuous relations) on a second countable, T0 space X either coincides with the Wadge reducibility for the given topology, or there is no topology on X that can turn it into Wadge reducibility.

Słowa kluczowe

EN

Wadge reducibility; relatively continuous relation

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2019
• Tom: Vol. 54
• Strony: 45--63
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Camerlo Riccardo

• Dipartimento di matematica Universita di Genova Via Dodecaneso 35, 16146 Genova — Italy

Bibliografia

• [1] M. de Brecht, Quasi-Polish spaces, Annals of Pure and Applied Logic 164 (2013), 356–381.
• [2] J. Duparc, Wadge hierarchy and Veblen hierarchy. Part I: Borel sets of finite rank, The Journal of Symbolic Logic 66 (2001), 56–86.
• [3] J. Duparc, K. Fournier, The Baire space and reductions by relatively continuous relations, preprint.
• [4] A.S. Kechris, Classical descriptive set theory, Springer, 1995.
• [5] Y. Pequignot, A Wadge hierarchy for second countable spaces, Archive for Mathematical Logic 54 (2015), 659–683.
• [6] P. Schlicht, Continuous reducibility and dimension of metric spaces, Archive for Mathematical Logic 57 (2018), 329–359.
• [7] V.L. Selivanov, Difference hierarchy in ϕ-spaces, Algebra and Logic 43 (2004), 238–248.
• [8] A. Tang, Wadge reducibility and Hausdorff difference hierarchy in P ω, In: Continuous lattices (Ed. B. Banaschewski, R.-E. Hoffmann), Springer, 1981, pp. 360–371.
• [9] W.W. Wadge, Reducibility and determinateness on the Baire space, PhD thesis, University of California at Berkeley, 1983.
• [10] K. Weihrauch, Computable analysis: an introduction, Springer, 2000.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).