Abstract
We study, in the context of reverse mathematics, the strength of Ramseyan factorization theorem (\({\rm RF}^{s}_{k}\)), a Ramsey-type theorem used in automata theory. We prove that \({\rm RF}^s_k\) is equivalent to \({\rm RT}^2_2\) for all s,k ≥ 2, k ∈ ω over RCAo. We also consider a weak version of Ramseyan factorization theorem and prove that it is in between ADS and CAC.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cholak, P.A., Jockusch, C.G., Slaman, T.A.: On the strength of Ramsey’s theorem for pairs. Journal of Symbolic Logic 66(1), 1–55 (2001)
Chong, C.-T., Slaman, T.A., Yang, Y.: The metamathematics of stable Ramsey’s theorem for pairs (to appear)
Flood, S.: Reverse mathematics and a Ramsey-type König’s lemma. Journal of Symbolic Logic 77(4), 1272–1280 (2012)
H. Friedman, F. Pelupessy.: Independence of Ramsey theorem variants using ε 0. draft.
Hirschfeldt, D.R.: Slicing the truth: On the computability theoretic and reverse mathematical analysis of combinatorial principles (to appear)
Hirschfeldt, D.R., Shore, R.A.: Combinatorial principles weaker than Ramsey’s theorem for pairs. Journal of Symbolic Logic 72(1), 171–206 (2007)
Lerman, M., Solomon, R., Towsner, H.: Separating principles below ramsey’s theorem for pairs. Journal of Mathematical Logic 13(2), 1350007 (2013)
Perrin, D., Pin, J.-É.: Infinite Words: Automata, Semigroups, Logic and Games, vol. 141. Academic Press (2004)
Simpson, S.G.: Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic, 2nd edn., pp. XIV + 445 pages. Springer (1999); Perspectives in Logic, Association for Symbolic Logic. Cambridge University Press, pp. XVI+ 444 pages (2009)
Yokoyama, K.: Finite iterations of infinite and finite Ramsey’s theorem (in preparation)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Murakami, S., Yamazaki, T., Yokoyama, K. (2014). On the Ramseyan Factorization Theorem. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-08019-2_33
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08018-5
Online ISBN: 978-3-319-08019-2
eBook Packages: Computer ScienceComputer Science (R0)