# Definability of Recursive Predicates in the Induced Subgraph Order

Conference paper

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## Abstract

Consider the set of all finite simple graphs \(\mathcal {G}\) ordered by the induced subgraph order \(\le _i\). Building on previous work by Wires [14] and Jezek and Mckenzie [5, 6, 7, 8], we show that every recursive predicate over graphs is definable in the first order theory of (\(\mathcal {G},\le _i, P_3\)) where \(P_3\) is the path on 3 vertices.

## Keywords

Turing Machine Order Theory Label Graph Cardinality Constraint Connectivity Constraint
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

### Acknowledgment

I would like to thank my guide Prof. R. Ramanujam for his advice and discussions on both technical matter and the presentation of this paper.

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