Continuous reducibility: functions versus relations

Riccardo Camerlo

Abstrakt

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.

AMS subject classificastion: Primary 03E15; Secondary 03D55

Słowa kluczowe: Wadge reducibility, relatively continuous relation
References

[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 -spaces, Algebra and Logic 43 (2004), 238– 248.

[8] A. Tang,Wadge reducibility and Hausdorff difference hierarchy in P, 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.

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