### 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 |
---|---|

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

}

*Proceedings of the American Mathematical Society*, vol. 123, no. 10, pp. 3197-3204. https://doi.org/10.1090/S0002-9939-1995-1273503-6

**The borel classes of mahler’s a, s, t, and u numbers.** / Ki, Haseo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The borel classes of mahler’s a, s, t, and u numbers

AU - Ki, Haseo

PY - 1995/10

Y1 - 1995/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966238483&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966238483&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1995-1273503-6

DO - 10.1090/S0002-9939-1995-1273503-6

M3 - Article

AN - SCOPUS:84966238483

VL - 123

SP - 3197

EP - 3204

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -