Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T16:09:24.688Z Has data issue: false hasContentIssue false
  • English
  • Français

The logic of the reverse mathematics zoo

Published online by Cambridge University Press:  10 November 2016

GIOVANNA D'AGOSTINO Open the ORCID record for GIOVANNA D'AGOSTINO [Opens in a new window]  and
ALBERTO MARCONE Open the ORCID record for ALBERTO MARCONE [Opens in a new window]
GIOVANNA D'AGOSTINO
Affiliation:
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy Emails: [email protected], [email protected]
ALBERTO MARCONE
Affiliation:
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy Emails: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Building on previous work by Mummert et al. (2015, The modal logic of Reverse Mathematics. Archive for Mathematical54 (3–4) 425–437), we study the logic underlying the web of implications and non-implications which constitute the so called reverse mathematics zoo. We introduce a tableaux system for this logic and natural deduction systems for important fragments of the language.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 3: Mind, Mechanism and Mathematics: Computability Unchained , March 2018 , pp. 412 - 428
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ben-Ari, M. (2012) Mathematical Logic for Computer Science, 3rd edition, Springer, London.CrossRefGoogle Scholar
Belanger, D. R. (2015) WKL0 and induction principles in model theory. Annals of Pure and Applied Logic 166 (7–8) 767–799.CrossRefGoogle Scholar
Cholak, P., Marcone, A. and Solomon, R. (2004) Reverse mathematics and the equivalence of definitions for well and better quasi-orders. Journal of Symbolic Logic 69 (3) 683–712.CrossRefGoogle Scholar
Dzhafarov, D. D. Reverse Mathematics Zoo. Available at: http://rmzoo.math.uconn.edu/.Google Scholar
Friedman, H., Simpson, S. G. and Yu, X. (1993) Periodic points and subsystems of second-order arithmetic. Annals of Pure and Applied Logic 62 (1) 51–64, Logic Colloquium '89 (Berlin).CrossRefGoogle Scholar
Hirschfeldt, D. R. (2015) Slicing The Truth, volume 28 of Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore. World Scientific Publishing Co.Google Scholar
Hirschfeldt, D. R. and Shore, R. A. (2007) Combinatorial principles weaker than Ramsey's theorem for pairs. Journal of Symbolic Logic 72 (1) 171–206.CrossRefGoogle Scholar
Howard, P. Consequences of the Axiom of Choice Project Homepage. Available at: http://www.math.purdue.edu/~hrubin/JeanRubin/Papers/conseq.html.Google Scholar
Howard, P. and Rubin, J. E. (1998) Consequences of the Axiom of Choice, Mathematical Surveys and Monographs, volume 59, American Mathematical Society, Providence, RI, With 1 IBM-PC floppy disk (3.5 inch; WD).CrossRefGoogle Scholar
Huth, M. and Ryan, M. (2004) Logic in Computer Science, 2nd edition, Cambridge University Press, Cambridge. Modelling and reasoning about systems.CrossRefGoogle Scholar
Marcone, A. (2007) Interval orders and reverse mathematics. Notre Dame Journal of Formal Logic 48 (3) 425–448 (electronic).CrossRefGoogle Scholar
Marques-Silva, J. and Lynce, I. (2014) SAT solvers. In: Tractability, Cambridge University Press, Cambridge 331–349.CrossRefGoogle Scholar
Montalbán, A. (2011) Open questions in reverse mathematics. Bulletin of Symbolic Logic 17 (3) 431–454.CrossRefGoogle Scholar
Mummert, C., Saadaoui, A. and Sovine, S. (2015) The modal logic of Reverse Mathematics. Archive for Mathematical Logic 54 (3–4) 425–437.CrossRefGoogle Scholar
Nerode, A. and Shore, R. A. (1997) Logic for Applications, 2nd edition, Graduate Texts in Computer Science, Springer-Verlag, New York.CrossRefGoogle Scholar
Patey, L. Manually maintained Zoo. Available at: http://www.ludovicpatey.com/media/research/zoo.pdf.Google Scholar
Schöning, U. and Torán, J. (2013) The Satisfiability Problem, Mathematik für Anwendungen [Mathematics for Applications], volume 3, Lehmanns Media, Berlin. Algorithms and analyses, Translated from the 2011 German original.Google Scholar
Simpson, S. G. (2009) Subsystems of Second Order Arithmetic, 2nd edition, Perspectives in Logic, Cambridge University Press, Cambridge; Association for Symbolic Logic, Poughkeepsie, NY.CrossRefGoogle Scholar