Definability in First Order Theories of Graph Orderings

被引：4
|
作者：
Ramanujam, R. [1 ]
Thinniyam, R. S. [1 ]
机构：
[1] Inst Math Sci, Madras 600113, Tamil Nadu, India
来源：
LOGICAL FOUNDATIONS OF COMPUTER SCIENCE (LFCS 2016) | 2016年 / 9537卷
关键词：
Graphs; Partial order; Logical theory; Definability; SUBSTRUCTURE ORDERINGS; UNDECIDABILITY;
D O I：
10.1007/978-3-319-27683-0_23
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study definability in the first order theory of graph order: that is, the set of all simple finite graphs ordered by either the minor, subgraph or induced subgraph relation. We show that natural graph families like cycles and trees are definable, as also notions like connectivity, maximum degree etc. This naturally comes with a price: bi-interpretability with arithmetic. We discuss implications for formalizing statements of graph theory in such theories of order.
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页码：331 / 348
页数：18
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