Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Forcing with matrices of countable elementary submodels
HTML articles powered by AMS MathViewer

by Borisa Kuzeljevic and Stevo Todorcevic PDF
Proc. Amer. Math. Soc. 145 (2017), 2211-2222 Request permission

Abstract:

We analyze the forcing notion $\mathcal P$ of finite matrices whose rows consist of isomorphic countable elementary submodels of a given structure of the form $H_{\theta }$. We show that forcing with this poset adds a Kurepa tree $T$. Moreover, if $\mathcal P_c$ is a suborder of $\mathcal P$ containing only continuous matrices, then the Kurepa tree $T$ is almost Souslin, i.e., the level set of any antichain in $T$ is not stationary in $\omega _1$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E57
  • Retrieve articles in all journals with MSC (2010): 03E57
Additional Information
  • Borisa Kuzeljevic
  • Affiliation: Mathematical Institute SANU, Kneza Mihaila 36, 11001 Belgrade, Serbia
  • Email: borisa@mi.sanu.ac.rs
  • Stevo Todorcevic
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada, M5S 2E4 – and – Institut de Mathématiques de Jussieu, UMR 7586, 2 pl. Jussieu, Case 7012, 75251 Paris Cedex 05, France – and – Mathematical Institute SANU, Kneza Mihaila 36, 11001 Belgrade, Serbia
  • MR Author ID: 172980
  • Email: stevo@math.toronto.edu, stevo.todorcevic@imj-prg.fr, stevo@mi.sanu.ac.rs
  • Received by editor(s): March 28, 2015
  • Received by editor(s) in revised form: June 19, 2015, and September 2, 2015
  • Published electronically: January 26, 2017
  • Additional Notes: This paper was conceived during the Summer of 2014 when the first author was visiting Institut de Mathématiques de Jussieu. The first author would like to thank the Equipe de Logique of that Institute for support which made this visit possible. The first author was partially supported by the MPNTR grant ON174006
  • Communicated by: Mirna Džamonja
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2211-2222
  • MSC (2010): Primary 03E57
  • DOI: https://doi.org/10.1090/proc/13133
  • MathSciNet review: 3611332