Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-22T20:42:52.036Z Has data issue: false hasContentIssue false

Possible m-diagrams ofmodels of arithmetic

Published online by Cambridge University Press:  31 March 2017

By
Andrew Arana
Edited by
Stephen G. Simpson
Stephen G. Simpson
Affiliation:
Pennsylvania State University
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Reverse Mathematics 2001 , pp. 1 - 18
Publisher: Cambridge University Press
Print publication year: 2005

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

[1] Andrew, Arana, Solovay's theorem cannot be simplified, Annals of Pure and Applied Logic, vol. 112 (2001), pp. 27–41.Google Scholar
[2] Jon, Barwise (editor), Handbook of mathematical logic, Studies in Logic and the Foundations ofMathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977.
[3] Solomon, Feferman, Arithmetically definable models of formalizable arithmetic, Notices of the American Mathematical Society, vol. 5 (1958), p. 679.Google Scholar
[4] KurtGödel, Über formal unentscheidhare Sätze der PrincipiaMathematica und verwandter Systeme I,Collected works (Solomon Feferman et al., editors), vol. 1, Oxford University Press, New York and Oxford, 1986, pp. 145–195.
[5] Leo, Harrington, Building non-standard models of Peano Arithmetic, Unpublished notes, 1979.
[6] Julia F., Knight, True approximations and models of arithmetic, Models and computability (B., Cooper and J., Truss, editors), Cambridge University Press, New York, 1999, pp. 255–278.
[7] Angus, Macintyre and David, Marker, Degrees of recursively saturated models,Transactions of the American Mathematical Society, vol. 282 (1984), pp. 539–554.
[8] David, Marker, Degrees of models of true arithmetic,Proceedings of the Herbrand Symposium (J., Stern, editor), North-Holland, 1982, pp. 233–242.
[9] David, Marker, Degrees of models of arithmetic, Ph.D. thesis, Yale University, 1983.
[10] Yuri, Matijasevich, Enumerable sets are Diophantine,Doklady Akademii Nauka SSSR, vol. 191 (1970), pp. 272–282, Russian.
[11] J. B., Rosser, Extensions of some theorems of Gödel and Church,The Journal of Symbolic Logic, vol. 1 (1936), pp. 87–91.
[12] Dana, Scott, Algebras of sets binumerable in complete extensions of arithmetic,Recursive function theory(J., Dekker, editor), Proceedings of Symposia in Pure Mathematics, vol. V, American Mathematical Society, 1962, pp. 117–122.Google Scholar
[13] Stephen G., Simpson, Degrees of unsolvability: A survey of results, [2], pp. 631–652.
[14] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer, 1999.
[15] Robert, Solovay, Degrees of models of true arithmetic, Circulated preprint, 1982.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] 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 saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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
×

Save book to Dropbox

To save 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 saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save 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 saving content to Google Drive.

Available formats
×