### Abstract

In this article we examine the A, S, T, and U sets of Mahler's classification from a descriptive set theoretic point of view. We calculate the possible locations of these sets in the Borel hierarchy. A turns out to be - complete, while U provides a rare example of a natural Incomplete set- We produce an upperbound of Lj for S and show that T. Our main result is based on a deep theorem of Schmidt that allows us to guarantee the existence of the T numbers.

Original language | English |
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Pages (from-to) | 3197-3204 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 123 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1995 Oct |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics