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WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS. / Kihara, Takayuki; Selivanov, Victor.

In: Proceedings of the American Mathematical Society, Vol. 150, No. 9, 01.09.2022, p. 3989-4003.

Research output: Contribution to journal › Article › peer-review

Harvard

Kihara, T & Selivanov, V 2022, 'WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS', Proceedings of the American Mathematical Society, vol. 150, no. 9, pp. 3989-4003. https://doi.org/10.1090/proc/15930

APA

Kihara, T., & Selivanov, V. (2022). WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS. Proceedings of the American Mathematical Society, 150(9), 3989-4003. https://doi.org/10.1090/proc/15930

Vancouver

Kihara T, Selivanov V. WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS. Proceedings of the American Mathematical Society. 2022 Sep 1;150(9):3989-4003. https://doi.org/10.1090/proc/15930

Author

Kihara, Takayuki ; Selivanov, Victor. / WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS. In: Proceedings of the American Mathematical Society. 2022 ; Vol. 150, No. 9. pp. 3989-4003.

BibTeX

@article{1f5c9c77e7c64ecebabc70d9aae28e45,
title = "WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS",
abstract = "We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e., {0,1}-valued functions) to Q-valued functions, for a better quasiorder Q. In this article, we consider more general reducibilities on the Q-valued functions and generalise some results of L. Motto Ros [J. Symbolic Logic 74 (2009), pp. 27-49] in the first direction and of T. Kihara and A. Montalb{\'a}n [Trans. Amer. Math. Soc. 370 (2018), pp. 9025-9044] in the second direction: Our main result states that the structure of the Δ0α-degrees of Δ0α+γ-measurable Q-valued functions is isomorphic to the Δ0β-degrees of Δ0β+γ-measurable Q-valued functions, and these are isomorphic to the generalized homomorphism order on the γ-th iterated Q-labeled forests.",
keywords = "better quasiorder, Borel hierarchy, Wadge degree",
author = "Takayuki Kihara and Victor Selivanov",
year = "2022",
month = sep,
day = "1",
doi = "10.1090/proc/15930",
language = "English",
volume = "150",
pages = "3989--4003",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "9",

}

RIS

TY - JOUR

T1 - WADGE-LIKE DEGREES OF BOREL BQO-VALUED FUNCTIONS

AU - Kihara, Takayuki

AU - Selivanov, Victor

PY - 2022/9/1

Y1 - 2022/9/1

N2 - We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e., {0,1}-valued functions) to Q-valued functions, for a better quasiorder Q. In this article, we consider more general reducibilities on the Q-valued functions and generalise some results of L. Motto Ros [J. Symbolic Logic 74 (2009), pp. 27-49] in the first direction and of T. Kihara and A. Montalbán [Trans. Amer. Math. Soc. 370 (2018), pp. 9025-9044] in the second direction: Our main result states that the structure of the Δ0α-degrees of Δ0α+γ-measurable Q-valued functions is isomorphic to the Δ0β-degrees of Δ0β+γ-measurable Q-valued functions, and these are isomorphic to the generalized homomorphism order on the γ-th iterated Q-labeled forests.

AB - We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e., {0,1}-valued functions) to Q-valued functions, for a better quasiorder Q. In this article, we consider more general reducibilities on the Q-valued functions and generalise some results of L. Motto Ros [J. Symbolic Logic 74 (2009), pp. 27-49] in the first direction and of T. Kihara and A. Montalbán [Trans. Amer. Math. Soc. 370 (2018), pp. 9025-9044] in the second direction: Our main result states that the structure of the Δ0α-degrees of Δ0α+γ-measurable Q-valued functions is isomorphic to the Δ0β-degrees of Δ0β+γ-measurable Q-valued functions, and these are isomorphic to the generalized homomorphism order on the γ-th iterated Q-labeled forests.

KW - better quasiorder

KW - Borel hierarchy

KW - Wadge degree

UR - http://www.scopus.com/inward/record.url?scp=85133334471&partnerID=8YFLogxK

U2 - 10.1090/proc/15930

DO - 10.1090/proc/15930

M3 - Article

AN - SCOPUS:85133334471

VL - 150

SP - 3989

EP - 4003

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -

ID: 126984597