Two conjectures on the arithmetic in ℝ and ℂ†

Mathematical Logic Quarterly 56 (2):175-184 (2010)
  Copy   BIBTEX

Abstract

Let G be an additive subgroup of ℂ, let Wn = {xi = 1, xi + xj = xk: i, j, k ∈ {1, …, n }}, and define En = {xi = 1, xi + xj = xk, xi · xj = xk: i, j, k ∈ {1, …, n }}. We discuss two conjectures. If a system S ⊆ En is consistent over ℝ, then S has a real solution which consists of numbers whose absolute values belong to [0, 22n –2]. If a system S ⊆ Wn is consistent over G, then S has a solution ∈ n in which |xj| ≤ 2n –1 for each j.

Author's Profile

Analytics

Added to PP
2013-12-01

Downloads
1,508 (#8,960)

6 months
119 (#41,758)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?