Article contents
RAMSEY’S THEOREM FOR PAIRS AND K COLORS AS A SUB-CLASSICAL PRINCIPLE OF ARITHMETIC
Published online by Cambridge University Press: 19 June 2017
Abstract
The purpose is to study the strength of Ramsey’s Theorem for pairs restricted to recursive assignments of k-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number $k \ge 2$, Ramsey’s Theorem for pairs and recursive assignments of k colors is equivalent to the Limited Lesser Principle of Omniscience for ${\rm{\Sigma }}_3^0$ formulas over Heyting Arithmetic. Alternatively, the same theorem over intuitionistic arithmetic is equivalent to: for every recursively enumerable infinite k-ary tree there is some $i < k$ and some branch with infinitely many children of index i.
- Type
- Articles
- Information
- Copyright
- Copyright © The Association for Symbolic Logic 2017
References
REFERENCES
- 1
- Cited by