Beyond abstract elementary classes: On the model theory of geometric lattices

被引：6

作者：

Hyttinen, Tapani ^{[1
]}

Paolini, Gianluca ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2018年 / 169卷 / 02期

关键词：

Geometric lattices; Abstract elementary classes; Matroids; Classification theory; Independence; AMPLE;

D O I：

10.1016/j.apal.2017.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on Crapo's theory of one point extensions of combinatorial geometries, we find various classes of geometric lattices that behave very well from the point of view of stability theory. One of them, (K-3, <=), is omega-stable, it has a monster model and an independence calculus that satisfies all the usual properties of non-forking. On the other hand, these classes are rather unusual, e.g. in (K-3, <=) the Smoothness Axiom fails, and so (K-3, <=) is not an AEC. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：117 / 145

页数：29

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