Skip to main content Accessibility help
×
Home
Hostname: page-component-6c8bd87754-x25dq Total loading time: 0.342 Render date: 2022-01-20T02:21:48.963Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Forcing on Bounded Arithmetic

from Part I - Invited Papers

Published online by Cambridge University Press:  23 March 2017

Gaisi Takeuti
Affiliation:
University of Illinois
Masahiro Yasumoto
Affiliation:
Nagoya University
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Gödel '96
Logical Foundations of Mathematics, Computer Science and Physics - Kurt Gödel's Legacy
, pp. 120 - 138
Publisher: Cambridge University Press
Print publication year: 2017

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

Church, A.. Review of (Turing 1936). J. Symbolic Logic 42–3, 1 (1937).Google Scholar
Cook, S. and Aanderaa, S.. On the minimum computation time of functions. Trans. AMS 142 (1969), 291–314.Google Scholar
Courcelle, B.. Graph rewriting: An algebraic and logic approach. In Handbook of Theoretical Computer Science, van Leeuwen, J., Ed. Elsevier, Amsterdam, 1990, pp. 195–242.
Davis, M.. Computability and Undecidability. McGraw-Hill, 1958.
Gandy, R.. Church's thesis and principles for mechanisms. In The Kleene Symposium (Amsterdam, 1980), Barwise, Keisler, and Kunen, Eds., North-Holland, pp. 123–48.
Gandy, R.. The confluence of ideas in 1936. In The Universal Turing Machine - A Half Century Review, Herken, R., Ed. Oxford Univ. Press, 1988, pp. 55–111.
Gödel, K.. On undecidable propositions of formal mathematical systems (1934). In Gödel's Collected Works I, Feferman, S. et al., Eds. Oxford Univ. Press, New York, 1986, pp. 346–71.
Gödel, K.. Über die Lange von Beweisen (1936). In Gödel's Collected Works I. Oxford Univ. Press, New York, 1986, pp. 396–399.
Gödel, K.. Some remarks on the undecidability results (1972). In Gödel's Collected Works II. Oxford Univ. Press, New York, 1990, pp. 305–6.
Herron, T.. An alternative definition of pushout diagrams and their use in characterizing K-graph machines. Carnegie Mellon University, May 1995.
Kleene, S.. Introduction to Metamathematics. P. Noordhoíf N.V., 1952.
Kolmogorov, A. and Uspensky, V.. On the definition of an algorithm. AMS Translations 21, 2 (1963), 217–245.Google Scholar
Markov, A.. Theory of Algorithms. Academy of Sciences of the USSR, Moscow, 1954.
Mendelson, E.. Second thoughts about Church's thesis and mathematical proofs. J. Phil. 87, 5 (1990), 225–33.Google Scholar
Mundici, D. and Sieg, W.. Paper machines. Philosophic, Mathematica 3 (1995), 5–30.Google Scholar
Paterson, M., Fischer, M., and Meyer, A.. An improved overlap argument for on-line multiplication. In Complexity of Computation (Providence, RI, 1974), Karp, R., Ed., AMS, pp. 97–111.
Post, E.. Finite combinatory processes—formulation 1. J. Symbolic Logic 1 (1936), 103–5.Google Scholar
Post, E.. Recursive unsolvability of a problem of Thue. J. Symbolic Logic 12 (1947), 1–11.Google Scholar
Schönhage, A.. Storage modification machines. SIAM J. on Computing 9 (1980), 490–508.Google Scholar
Shepherdson, J.. Mechanisms for computing over arbitrary structures. In The Universal Turing Machine—A Half Century Review, Herken, R., Ed. Oxford Univ. Press, 1988, pp. 581–601.
Shepherdson, J. and Sturgis, H.. Computability of recursive functions. J. ACM 10 (1963), 217–55.Google Scholar
Sieg, W.. Mechanical procedures and mathematical experience. In Mathematics and Mind, George, A., Ed. Oxford Univ. Press, 1994, pp. 71–117.
Turing, A.. On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc., series 2 42 (1936–7), 230–265.Google Scholar
Turing, A.. The word problem in semi-groups with cancellation. Ann. of Math. 52 (1950), 491–505.Google Scholar
Turing, A.. Solvable and unsolvable problems. Science News 31 (1953), 7–23.Google Scholar
Uspensky, V.. Kolmogorov and mathematical logic. J. Symbolic Logic 57 (1992), 385–412.Google Scholar
Uspensky, V. and Semenov, A.. What are the gains of the theory of algorithms: Basic developments connected with the concept of algorithm and with its application in mathematics. In Algorithms in Modern Mathematics and Computer Science (Berlin, 1981), Ershov, A. and Knuth, D., Eds., Springer-Verlag, pp. 100–235.

Send book to Kindle

To send this book 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.

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.

Available formats
×

Send book to Dropbox

To send content items to your account, please 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 account. Find out more about sending content to Dropbox.

Available formats
×

Send book to Google Drive

To send content items to your account, please 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 account. Find out more about sending content to Google Drive.

Available formats
×