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Transactions of the American Mathematical Society

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On the structure of the Wadge degrees of bqo-valued Borel functions


Authors: Takayuki Kihara and Antonio Montalbán
Journal: Trans. Amer. Math. Soc. 371 (2019), 7885-7923
MSC (2010): Primary 03E15; Secondary 03D55, 03D80
DOI: https://doi.org/10.1090/tran/7621
Published electronically: February 14, 2019
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Abstract: In this article, we give a full description of the Wadge degrees of Borel functions from $ \omega ^\omega $ to a better-quasi-ordering $ \mathcal {Q}$. More precisely, for any countable ordinal $ \xi $, we show that the Wadge degrees of $ \mathbf {\Delta }^0_{1+\xi }$-measurable functions $ \omega ^\omega \to \mathcal {Q}$ can be represented by countable joins of the $ \xi $th transfinite nests of $ \mathcal {Q}$-labeled well-founded trees.


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Additional Information

Takayuki Kihara
Affiliation: Graduate School of Informatics, Nagoya University, Nagoya, 464-8601, Japan
Email: kihara@i.nagoya-u.ac.jp

Antonio Montalbán
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: antonio@math.berkeley.edu

DOI: https://doi.org/10.1090/tran/7621
Received by editor(s): May 21, 2017
Received by editor(s) in revised form: April 15, 2018
Published electronically: February 14, 2019
Additional Notes: The first-named author was partially supported by JSPS KAKENHI grant 17H06738, 15H03634, and the JSPS Core-to-Core Program (A. Advanced Research Networks).
The second-named author was partially supported by NSF grant DMS-0901169 and the Packard Fellowship.
Article copyright: © Copyright 2019 American Mathematical Society