## Forcing with matrices of countable elementary submodels

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- 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

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## 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