Square principles with tail-end agreement

Archive for Mathematical Logic 54 (3-4):439-452 (2015)
  Copy   BIBTEX

Abstract

This paper investigates the principles □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{{\rm ta}}}_{\lambda,\delta}}$$\end{document}, weakenings of □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document} which allow δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta}$$\end{document} many clubs at each level but require them to agree on a tail-end. First, we prove that □λ,<ωta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$\end{document} implies □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document}. Then, by forcing from a model with a measurable cardinal, we show that □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,2}}$$\end{document} does not imply □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\lambda,\delta}}$$\end{document} for regular λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document}, and □δ+,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\delta^+,\delta}}$$\end{document} does not imply □δ+,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\delta^+,< \delta}}$$\end{document}. With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,\delta}}$$\end{document} does not imply □λ,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,< \delta}}$$\end{document} for δ<λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta < \lambda}$$\end{document}.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,069

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

Separating weak partial square principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.
Squares and covering matrices.Chris Lambie-Hanson - 2014 - Annals of Pure and Applied Logic 165 (2):673-694.
Rationality in Agreement.Gilbert Harman - 1988 - Social Philosophy and Policy 5 (2):1.
Chang’s Conjecture and weak square.Hiroshi Sakai - 2013 - Archive for Mathematical Logic 52 (1-2):29-45.
The traditional square of opposition.Terence Parsons - 2008 - Stanford Encyclopedia of Philosophy.
MRP , tree properties and square principles.Remi Strullu - 2011 - Journal of Symbolic Logic 76 (4):1441-1452.
Is an agreement an exchange of intentions?Joe Mintoff - 2004 - Pacific Philosophical Quarterly 85 (1):44–67.
Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
A relative of the approachability ideal, diamond and non-saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.

Analytics

Added to PP
2015-03-22

Downloads
17 (#765,400)

6 months
1 (#1,149,473)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Fresh subsets of ultrapowers.Assaf Shani - 2016 - Archive for Mathematical Logic 55 (5-6):835-845.

Add more citations

References found in this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Combinatorial principles in the core model for one Woodin cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Separating weak partial square principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.

Add more references