Interpretations in trees with countably many branches Conference Paper

Author(s): Rabinovich, Alexander; Rubin, Sasha
Title: Interpretations in trees with countably many branches
Title Series: LICS
Affiliation IST Austria
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.
Keywords: Composition method; finite-set interpretations; infinite scattered trees; monadic second order logic
Conference Title: Unknown
Conference Dates: June 25 - 28, 2012
Conference Location: Dubrovnik, Croatia
Publisher: IEEE  
Date Published: 2012-01-01
Start Page: 551
End Page: 560
DOI: 10.1109/LICS.2012.65
Open access: no
IST Austria Authors
  1. Sasha Rubin
    5 Rubin
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