Büchi Sequences in Local Fields and Local Rings

Volume 58 / 2010

Jerzy Browkin Bulletin Polish Acad. Sci. Math. 58 (2010), 109-115 MSC: Primary 11B83; Secondary 11Sxx. DOI: 10.4064/ba58-2-2


We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring ${\mathbb Z}_p$ of $p$-adic integers. In ${\mathbb Z}_p$ there are only finite but arbitrarily long Büchi sequences.


  • Jerzy BrowkinInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland

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