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rooted tree; unprovability; Kirby--Paris Theorem

References:

[1] Kirby L., Paris J.: **Accessible independence results for Peano Arithmetic**. Bulletin of the London Math. Soc 14, 1982. MR 0663480 | Zbl 0501.03017

[2] Loebl M.: **Hercules and Hydra, the game on rooted finite trees**. Comment. Math. Univ. Carolinae 26 (1985), 259-267. MR 0803922

[3] Loebl M.: **Hercules and Hydra**. Comment. Math. Univ. Carolinae 29 (1988), 85-95. MR 0937552 | Zbl 0666.05024

[4] Buchholz W., Wainer S.: **Provably computable functions and the fast growing hierarchy**. in: {Logic and Combinatorics}, Contemporary Mathematics, vol. 65, AMS 1986. MR 0891248 | Zbl 0635.03056