✦ LIBER ✦

Worms, gaps, and hydras

✍ Scribed by Lorenzo Carlucci

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 173 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410035

No coin nor oath required. For personal study only.

✦ Synopsis

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to Lev Beklemishev is also presented.

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