Abstract
An @1-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But fifteen years after Tennenbaum and Jech independently devised notions of forcing for introducing such a tree, Shelah proved that already the simplest forcing notion-Cohen forcing-adds an @1-Souslin tree. In this article, we identify a rather large class of notions of forcing that, assuming a GCH-type hypothesis, add λ+ C-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.
| Original language | English |
|---|---|
| Pages (from-to) | 437-455 |
| Number of pages | 19 |
| Journal | Notre Dame Journal of Formal Logic |
| Volume | 60 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 by University of Notre Dame.
Funding
This work was partially supported by the Israel Science Foundation grant 1630=14. The main results of this article were presented by the first author at the Toronto Set-Theory Seminar, October 2016, and by the second author at the Association for Symbolic Logic North American Meeting, Boise, March 2017.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 1630=14 |
Keywords
- Cohen forcing
- Hechler forcing
- Magidor forcing
- Microscopic approach
- Outside guessing of clubs
- Parameterized proxy principle
- Prikry forcing
- Radin forcing
- Souslin-tree construction
- square principle