title: A proof of Bel’tyukov—Lipshitz theorem by quasi-quantifier elimination. II. The main reduction
metadata.name: dc.contributor.author
metadata.value: Starchak, Mikhail R.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-16T19:22:02Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-16T19:22:02Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Starchak M. R. A proof of Bel’tyukov—Lipshitz theorem by quasi-quantifier elimination. II. The main reduction. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 608–619.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.406
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35108
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper is the second part of a new proof of the Bel’tyukov—Lipshitz theorem,
  which states that the existential theory of the structure  Z; 0, 1,+,−,≤, |  is decidable.
  We construct a quasi-quantifier elimination algorithm (the notion was introduced in the
  first part of the proof) to reduce the decision problem for the existential theory of
   Z; 0, 1,+,−,≤,GCD  to the decision problem for the positive existential theory of the
  structure  Z>0; 1, {a·}a∈Z>0 ,GCD . Since the latter theory was proved decidable in the
  first part, this reduction completes the proof of the theorem. Analogues of two lemmas
  of Lipshitz’s proof are used in the step of variable isolation for quasi-elimination. In the
  quasi-elimination step we apply GCD-Lemma, which was proved in the first part.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: quantifier elimination
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: existential theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: divisibility
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: decidability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chinese remainder theorem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A proof of Bel’tyukov—Lipshitz theorem by quasi-quantifier elimination. II. The main reduction
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 608-619.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35108/1/608-619.pdf
resources.format: Adobe PDF
resources.size: 337,63 kB