The monadic second-order logic of graphs IX: machines and their behaviours
Selected papers of the workshop on Topology and completion in semantics
On Infinite Terms Having a Decidable Monadic Theory
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
On decidability of monadic logic of order over the naturals extended by monadic predicates
Information and Computation
Expressing Cardinality Quantifiers in Monadic Second-Order Logic over Trees
Fundamenta Informaticae - Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa
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We study the expressive power of logical interpretations on the class of scattered trees, namely those with countably many infinite branches. Scattered trees can be thought of as the tree analogue of scattered linear orders. Every scattered tree has an ordinal rank that reflects the structure of its infinite branches. We prove, roughly, that trees and orders of large rank cannot be interpreted in scattered trees of small rank. We consider a quite general notion of interpretation: each element of the interpreted structure is represented by a set of tuples of subsets of the interpreting tree. Our trees are countable, not necessarily finitely branching, and may have finitely many unary predicates as labellings. We also show how to replace injective set-interpretations in (not necessarily scattered) trees by âfinitary' set-interpretations.