Free abelian lattice-ordered groups

被引：6
|
作者：
Glass, AMW
Macintyre, A
Point, F
机构：
[1] CMS, DPMMS, Cambridge CB3 0WB, England
[2] Univ Edinburgh, Dept Math & Stat, Edinburgh EH9 3JZ, Midlothian, Scotland
[3] Univ Mons, Inst Math & Informat, B-7000 Mons, Belgium
来源：
ANNALS OF PURE AND APPLIED LOGIC | 2005年 / 134卷 / 2-3期
关键词：
free abelian lattice-ordered groups; elementary equivalence; decidability; simplices;
D O I：
10.1016/j.apal.2004.10.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let n be a positive integer and FAl(n) be the free abelian lattice-ordered group on n generators. We prove that FAl(m) and FAl(n) do not satisfy the same first-order sentences in the language L = {+, -, 0, boolean AND,boolean OR } if m not equal n. We also show that Th(FAl(n)) is decidable iff n is an element of {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. (c) 2004 Elsevier B.V. All rights reserved.
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页码：265 / 283
页数：19
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