A forcing notion related to Hindman’s theorem

Archive for Mathematical Logic 54 (1-2):133-159 (2015)
  Copy   BIBTEX

Abstract

We give proofs of Ramsey’s and Hindman’s theorems in which the corresponding homogeneous sets are found with a forcing argument. The object of this paper is the study of the partial order involved in the proof of Hindman’s theorem. We are going to denote it by PFIN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}PFIN{\mathbb{P}_{FIN}}\end{document}. As a main result, we prove that Mathias forcing does not add Matet reals, which implies that PFIN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}PFIN{\mathbb{P}_{FIN}}\end{document} is not equivalent to Mathias forcing.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 104,804

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Maximally embeddable components.Miloš S. Kurilić - 2013 - Archive for Mathematical Logic 52 (7-8):793-808.
Isomorphic and strongly connected components.Miloš S. Kurilić - 2015 - Archive for Mathematical Logic 54 (1-2):35-48.
Mathias forcing and ultrafilters.Janusz Pawlikowski & Wojciech Stadnicki - 2016 - Archive for Mathematical Logic 55 (7-8):857-865.

Analytics

Added to PP
2015-09-03

Downloads
21 (#1,100,941)

6 months
4 (#1,018,094)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Forcing and stable ordered–union ultrafilters.Todd Eisworth - 2002 - Journal of Symbolic Logic 67 (1):449-464.
Some filters of partitions.Pierre Matet - 1988 - Journal of Symbolic Logic 53 (2):540-553.

Add more references