Skip to main content Accessibility help
×
Home
Hostname: page-component-747cfc64b6-xl4lj Total loading time: 0.247 Render date: 2021-06-14T10:16:32.386Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories

Published online by Cambridge University Press:  12 March 2014

Leszek Aleksander Kołodziejczyk
Affiliation:
Warsaw University, Institute of Mathematics, Banacha 2, 02-097 Warszawa, Poland. E-mail: lak@mimuw.edu.pl
Corresponding
E-mail address:

Abstract

Modifying the methods of Z. Adamowicz's paper Herbrand consistency and bounded arithmetic [3] we show that there exists a number n such that ⋃mSm (the union of the bounded arithmetic theories Sm) does not prove the Herbrand consistency of the finitely axiomatizable theory S3n

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2006

Access options

Get access to the full version of this content by using one of the access options below.

References

[1]Adamowicz, Z., private communication.Google Scholar
[2]Adamowicz, Z., On tableaux consistency in weak theories, Preprint 618, Institute of Mathematics of the Polish Academy of Sciences, 2001.Google Scholar
[3]Adamowicz, Z., Herbrand consistency and bounded arithmetic, Fundamenta Mathematicae, vol. 171 (2002), pp. 279292.CrossRefGoogle Scholar
[4]Adamowicz, Z. and Zbierski, P., On Herbrand consistency in weak arithmetic, Archive for Mathematical Logic, vol. 40 (2001). pp. 399413.CrossRefGoogle Scholar
[5]Buss, S. R. and Ignjatović, A., Unprovability of consistency statements in fragments of bounded arithmetic, Annals of Pure and Applied Logic, vol. 74 (1995), pp. 221–244.CrossRefGoogle Scholar
[6]Hájek, P. and Pudlák, P., Metamathematics of First-Order Arithmetic. Springer-Verlag, 1993.CrossRefGoogle Scholar
[7]Kraíček, J., Bounded Arithmetic, Propositional Logic, and Complexity Theory, Cambridge University Press, 1995.CrossRefGoogle Scholar
[8]Pudlák, P., Cuts, consistency statements, and interpretations, this Journal, vol. 50 (1985), pp. 423441.Google Scholar
[9]Pudlák, P., A note on bounded arithmetic, Fundamenta Mathematicae, vol. 136 (1990), pp. 8589.CrossRefGoogle Scholar
[10]Pudlák, P., Consistency and games, Logic colloquium '03 (Stoltenberg-Hansen, V. and Väänänen, J., editors), Lecture Notes in Logic, vol. 24, ASL and AK Peters, 2006, pp. 244281.Google Scholar
[11]Wilkie, A. J. and Paris, J. B., On the scheme of induction for bounded arithmetic formulas, Annals of Pure and Applied Logic, vol. 35 (1987), pp. 261302.CrossRefGoogle Scholar
[12]Wilkie, A. J. and Paris, J. B., On the existence of end-extensions of models of bounded induction, Logic, Methodology, and Philosophy of Science VIII (Moscow 1987) (Fenstad, J. E., Frolov, I. T., and Hilpinen, R.. editors), North-Holland, 1989, pp. 143161.Google Scholar
[13]Willard, D. E., How to extend the semantic tableaux and cut-free versions of the second incompleteness theorem almost to Robinson's arithmetic Q. this Journal, vol. 67 (2002). pp. 465496.Google Scholar
5
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

On the Herbrand notion of consistency for finitely axiomatizable fragments of bounded arithmetic theories
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *