A Constructive Version of the Hilbert Basis Theorem

@inproceedings{May2004ACV,
  title={A Constructive Version of the Hilbert Basis Theorem},
  author={Aaron May},
  year={2004}
}
The Hilbert Basis Theorem was the first major example of a non-constructive proof recognized in mathematics. Gordan said, on the subject of the theorem, “das ist keine Mathematik, das ist Theologie!” — “this is not Mathematics, this is Theology!” [8] Although there are several equivalent statements of the theorem, in this paper we will consider the version which states, in essence, that all rings of polynomials over countable fields are finitely generated. (More generally, the theorem holds for… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-4 OF 4 CITATIONS

A bound for Dickson's lemma

  • Logical Methods in Computer Science
  • 2015
VIEW 2 EXCERPTS
CITES METHODS
HIGHLY INFLUENCED

Human Rationality Challenges Universal Logic

  • Logica Universalis
  • 2010
VIEW 1 EXCERPT
CITES BACKGROUND

The metamathematics of ergodic theory

  • Ann. Pure Appl. Logic
  • 2009
VIEW 1 EXCERPT
CITES BACKGROUND

P I C C P M

VIEW 1 EXCERPT
CITES BACKGROUND

References

Publications referenced by this paper.
SHOWING 1-8 OF 8 REFERENCES

Ordinal Numbers and the Hilbert Basis Theorem

  • J. Symb. Log.
  • 1988
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Zur intuitionistischen Arithmetik und Zahlentheorie

K Gödel
  • Ergebnisse eines mathematischen Kolloquiums, 4:34–38, 1933.
  • 1933
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

Similar Papers