Monotone subsequence via ultrapower-Reference-Cited by-同舟云学术

Monotone subsequence via ultrapower

Published:2018-01-01 Issue:1 Volume:16 Page:149-153
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Błaszczyk Piotr¹,Kanovei Vladimir²,Katz Mikhail G.³,Nowik Tahl³

Affiliation:

1. Institute of Mathematics , Pedagogical University of Cracow , Cracow , Poland

2. IPPI, Moscow, and MIIT , Moscow , Russia

3. Department of Mathematics , Bar Ilan University , Ramat Gan , 52900 , Israel

Abstract

Abstract An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2018-0015/pdf

Reference6 articles.

1. Tao T., Hilbert’s fifth problem and related topics, Graduate Studies in Mathematics, 153, American Mathematical Society, Providence, RI, 2014.

2. Hirshfeld J., Nonstandard combinatorics, Studia Logica, 1988, 47, no. 3, 221–232.

3. Newman D., A problem seminar, Problem Books in Mathematics, Springer-Verlag, New York-Berlin, 1982.

4. Fletcher P., Hrbacek K., Kanovei V., Katz M., Lobry C., Sanders S., Approaches to analysis with infinitesimals following Robinson, Nelson, and others, Real Analysis Exchange 2017, 42, no. 2, 193–252. See https://arxiv.org/abs/1703.00425 and http://msupress.org/journals/issue/?id=50-21D-61F

5. Herzberg F., Kanovei V., Katz M., Lyubetsky V., Minimal axiomatic frameworks for definable hyperreals with transfer, Journal of Symbolic Logic, to appear. See https://arxiv.org/abs/1707.00202 and http://dx.doi.org/10.1017/jsl.2017.48