Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Hércules contra la Hidra y la muerte del Internet
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Keywords

Hercules
the Hydra
Goodstein sequences
Internet
ordinals numbers
Peano’s Arithmetic
Hércules
la Hidra
sucesiones de Goodstein
Internet
números ordinales
Aritmética de Peano

How to Cite

Piza Volio, E. (2004). Hércules contra la Hidra y la muerte del Internet. Revista De Matemática: Teoría Y Aplicaciones, 11(1), 1–16. https://doi.org/10.15517/rmta.v11i1.234

Abstract

Hercules killed the Hydra of Lerna in a bloody battle—the second of the labor tasks imposed upon him in atonement for his hideous crimes. The Hydra was a horrible, aggressive mythological monster with many heads and poisonous blood, whose heads multiplied each time one of them was severed. This article explores some mathematical methods about this interesting epic battle. A generalization of the original Kirby & Paris model is proposed. We also study the connection of this model with Goodstein ultra-growing and recursive sequences. As an interesting application, we next analyze the inevitable death of another huge monster of our modern era: the Internet.

https://doi.org/10.15517/rmta.v11i1.234
PDF (Español (España))

References

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Ketonen, J.; Solovay, R. (1981) “Rapidly growing Ramsey functions”, Annals of Mathematics 113: 267–314.

Kirby, L.; Paris, J. (1982) “Accessible independence results for Peano arithmetic”, Bulletin of the London Mathematical Society 14: 285–293.

Loebl, M. (1988) “Hercules and Hydra”, Commentationes Mathematicae Univesitatis Carolinae 29(1), 85–95.

Luccio, F.; Pagli, L. (2000) “Death of a monster”, Pre-print, Departamento de Informática de la Universidad de Pisa, Italia.

Matousek, J.; Loebl, M. (1991) “Hercules versus hidden Hydra helper”, Commentationes Mathematicae Univesitatis Carolinae 32(4): 731–741.

Misercque, D. (1990) “Le plus long combat d’Hercule”, Bulletin de la Société Mathématique de Belgique 42, série B: 319–331.

Monk, D.J. (1969) Introduction to Set Theory. McGraw-Hill Book Company, New York.

Rogers, H. (1967) Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Company, New York.

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