DS-2009-03:
Semmes, Brian Thomas
(2009)
*A Game for the Borel Functions.*
Doctoral thesis, University of Amsterdam.

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## Abstract

In this thesis, we deal with classes of functions on Baire space. For

some important function classes, game representations are known and

proved to be very useful. The most prominent example is Wadge’s

characterization of the continuous func- tions that allowed the

development of the theory of the Wadge hierarchy; in 2006, based on a

result of Jayne and Rogers, Andretta gave a game representation for

the ∆1 functions (in the language of this thesis, this is the class

Λ2,2 ). Game characterizations are important as they allow for

“Wadge-style proof techniques”.

In their paper on Borel functions, Andretta and Martin lament that

“there is no analogue of the Wadge/Lipschitz games for Borel functions,

[and] hence many of the standard proofs for the Wadge hierarchy do not

generalize in a straightforward way to the Borel set-up.”

This suggested two important questions:

1. Can similar characterizations be given for other function

classes, most notably for the class of all Borel functions and the

class Λ3,3 ?

2. Is there an analogue of the Jayne-Rogers theorem at the third

level of the Borel hierarchy?

In this thesis, we give positive answers to these questions.

Keywords:

Item Type: | Thesis (Doctoral) |
---|---|

Report Nr: | DS-2009-03 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 2009 |

Subjects: | Language |

Depositing User: | Dr Marco Vervoort |

Date Deposited: | 14 Jun 2022 15:16 |

Last Modified: | 14 Jun 2022 15:16 |

URI: | https://eprints.illc.uva.nl/id/eprint/2073 |

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