Interpretations in trees with countably many branches

A. Rabinovich, S. Rubin, in:, IEEE, 2012.


Conference Paper | Published | English
Author
;
Department
Series Title
LICS
Abstract
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.
Publishing Year
Date Published
2012-01-01
Article Number
6280474
Conference
LICS: Symposium on Logic in Computer Science
Conference Location
Dubrovnik, Croatia
Conference Date
2012-06-25 – 2012-06-28
IST-REx-ID

Cite this

Rabinovich A, Rubin S. Interpretations in trees with countably many branches. In: IEEE; 2012. doi:10.1109/LICS.2012.65
Rabinovich, A., & Rubin, S. (2012). Interpretations in trees with countably many branches. Presented at the LICS: Symposium on Logic in Computer Science, Dubrovnik, Croatia: IEEE. https://doi.org/10.1109/LICS.2012.65
Rabinovich, Alexander, and Sasha Rubin. “Interpretations in Trees with Countably Many Branches.” IEEE, 2012. https://doi.org/10.1109/LICS.2012.65.
A. Rabinovich and S. Rubin, “Interpretations in trees with countably many branches,” presented at the LICS: Symposium on Logic in Computer Science, Dubrovnik, Croatia, 2012.
Rabinovich A, Rubin S. 2012. Interpretations in trees with countably many branches. LICS: Symposium on Logic in Computer Science, LICS,
Rabinovich, Alexander, and Sasha Rubin. Interpretations in Trees with Countably Many Branches. 6280474, IEEE, 2012, doi:10.1109/LICS.2012.65.

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