TY - GEN

T1 - Interpretations in trees with countably many branches

AU - Rabinovich, Alexander

AU - Rubin, Sasha

PY - 2012

Y1 - 2012

N2 - 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 'finitary' set-interpretations.

AB - 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 'finitary' set-interpretations.

KW - Composition method

KW - finite-set interpretations

KW - infinite scattered trees

KW - monadic second order logic

UR - http://www.scopus.com/inward/record.url?scp=84867160243&partnerID=8YFLogxK

U2 - 10.1109/LICS.2012.65

DO - 10.1109/LICS.2012.65

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AN - SCOPUS:84867160243

SN - 9780769547695

T3 - Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012

SP - 551

EP - 560

BT - Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012

T2 - 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012

Y2 - 25 June 2012 through 28 June 2012

ER -