1. Order-Invariant Types and Their Applications
- Author
-
Pablo Barcelo and Leonid Libkin
- Subjects
computer science - logic in computer science ,Logic ,BC1-199 ,Electronic computers. Computer science ,QA75.5-76.95 - 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.
- Published
- 2016
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