@Article{         10.2307/1996110,
  Author        = "Seidenberg, A.",
  Abstract      = "In a previous note it was shown that if a bound f(i) is placed on the degrees of the elements in some basis of an ideal Ai in the polynomial ring k[ X1, ..., Xn ] over an explicitly given field k, i = 0, 1, 2, ..., then a bound can be (and was) constructed for the length of a strictly ascending chain $A\_0 < A\_1 < \cdots$. This result is now obtained using a strictly finitist argument. A corollary is a finitist version of Hilbert's theorem on ascending chains.",
  date-added    = "2023-02-20 12:04:39 +0100",
  date-modified = "2023-02-20 12:04:39 +0100",
  ISSN          = "00029947",
  Journal       = "Transactions of the American Mathematical Society",
  Pages         = "305--312",
  Publisher     = "American Mathematical Society",
  Title         = "Constructive Proof of Hilbert's Theorem on Ascending Chains",
  URL           = "http://www.jstor.org/stable/1996110",
  URLDate       = "2023-02-18",
  Volume        = "174",
  Year          = "1972",
  bdsk-url-1    = "http://www.jstor.org/stable/1996110",
  File          = "Constructive Proof of Hilbert's Theorem on Ascending Chains - seidenberg1972 - a.pdf"
}

@Article{ 10.2307/1996110, Author = "Seidenberg, A.", Abstract = "In a previous note it was shown that if a bound f(i) is placed on the degrees of the elements in some basis of an ideal Ai in the polynomial ring k[ X1, ..., Xn ] over an explicitly given field k, i = 0, 1, 2, ..., then a bound can be (and was) constructed for the length of a strictly ascending chain $A_0 < A_1 < \cdots$. This result is now obtained using a strictly finitist argument. A corollary is a finitist version of Hilbert's theorem on ascending chains.", date-added = "2023-02-20 12:04:39 +0100", date-modified = "2023-02-20 12:04:39 +0100", ISSN = "00029947", Journal = "Transactions of the American Mathematical Society", Pages = "305--312", Publisher = "American Mathematical Society", Title = "Constructive Proof of Hilbert's Theorem on Ascending Chains", URL = "http://www.jstor.org/stable/1996110", URLDate = "2023-02-18", Volume = "174", Year = "1972", bdsk-url-1 = "http://www.jstor.org/stable/1996110", File = "Constructive Proof of Hilbert's Theorem on Ascending Chains - seidenberg1972 - a.pdf" }