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- Title
First-order aspects of tree paths.
- Authors
KELLERMAN, RUAAN
- Abstract
Tree paths are investigated using first-order logic. The following results are obtained: (i) every definable path can be defined by a first-order formula using at most one parameter chosen from the path itself; (ii) a canonical representation of the formulas that define definable paths is obtained; and (iii) every tree that has only finitely many paths that are not definable is n-equivalent to a tree of which all paths are definable. Moreover, a certain property that might be expected to hold, involving the transfer of n-equivalence between trees, is shown not to be true.
- Subjects
TREE graphs; FIRST-order logic; MODERN logic; MATHEMATICAL logic; MATHEMATICAL equivalence
- Publication
Logic Journal of the IGPL, 2015, Vol 23, Issue 4, p688
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzv026