A computable analysis of variable words theorems
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- by Lu Liu, Benoit Monin and Ludovic Patey PDF
- Proc. Amer. Math. Soc. 147 (2019), 823-834 Request permission
Abstract:
The Carlson–Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, there is an infinite sequence with infinitely many variables such that for every valuation, some specific set of initial segments is homogeneous. Friedman, Simpson, and Montalban asked about its reverse mathematical strength. We study the computability-theoretic properties and the reverse mathematics of this statement, and relate it to the finite union theorem. In particular, we prove the Ordered Variable word for binary strings in $\textsf {ACA}_0$.References
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Additional Information
- Lu Liu
- Affiliation: Department of Mathematics, Central South University, ChangSha 410083, People’s Republic of China
- MR Author ID: 980145
- Email: g.jiayi.liu@gmail.com
- Benoit Monin
- Affiliation: Département d’Informatique, Faculté des Sciences et Technologie, LACL, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
- MR Author ID: 1024056
- Email: benoit.monin@computability.fr
- Ludovic Patey
- Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
- MR Author ID: 1102703
- ORCID: 0000-0002-0304-7926
- Email: ludovic.patey@computability.fr
- Received by editor(s): November 6, 2017
- Received by editor(s) in revised form: November 7, 2017, May 20, 2018, and June 2, 2018
- Published electronically: November 5, 2018
- Communicated by: Heike Mildenberger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 823-834
- MSC (2010): Primary 03B30
- DOI: https://doi.org/10.1090/proc/14269
- MathSciNet review: 3894920