Order-Invariant Types and Their Applications
Logic in Computer Science
2017-01-11 v3
Abstract
Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide two applications of this notion. One is a proof, from the basic principles, of a theorem by Courcelle stating that over trees, order-invariant MSO properties are expressible in MSO with counting quantifiers. The other is an analog of the Feferman-Vaught theorem for order-invariant properties.
Cite
@article{arxiv.1603.04309,
title = {Order-Invariant Types and Their Applications},
author = {Pablo Barcelo and Leonid Libkin},
journal= {arXiv preprint arXiv:1603.04309},
year = {2017}
}