Reverse mathematics of the finite downwards closed subsets of ordered by inclusion and adjacent Ramsey for fixed dimension

Mathematical Logic Quarterly 64 (3):178-182 (2018)
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Abstract

We show that the well partial orderedness of the finite downwards closed subsets of, ordered by inclusion, is equivalent to the well foundedness of the ordinal. Since we use Friedman's adjacent Ramsey theorem for fixed dimensions in the upper bound, we also give a treatment of the reverse mathematical status of that theorem.

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10.1002/malq.201700040

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
On the restricted ordinal theorem.R. L. Goodstein - 1944 - Journal of Symbolic Logic 9 (2):33-41.
Ordinal numbers and the Hilbert basis theorem.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (3):961-974.

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