Notre Dame Journal of Formal Logic 60 (3):437-455 (2019)

Abstract
An ℵ1-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 ℵ1-Souslin tree.In this article, we identify a rather large class of notions of forcing that, assuming a GCH-type hypothesis, add a λ+-Souslin tree. This class includes Prikry, Magidor, and Radin forcing.
Keywords Cohen forcing   Hechler forcing   Magidor forcing   Prikry forcing   Radin forcing   microscopic approach   outside guessing of clubs   parameterized proxy principle   square principle  Souslin-tree construction
Categories (categorize this paper)
DOI 10.1215/00294527-2019-0011
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,410
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Squares, Scales and Stationary Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, Squares and Reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Aronszajn Trees, Square Principles, and Stationary Reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.

View all 10 references / Add more references

Citations of this work BETA

A Microscopic Approach to Souslin-Tree Construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
Souslin Trees at Successors of Regular Cardinals.Assaf Rinot - 2019 - Mathematical Logic Quarterly 65 (2):200-204.

Add more citations

Similar books and articles

An Variation for One Souslin Tree.Paul Larson - 1999 - Journal of Symbolic Logic 64 (1):81-98.
An $Mathbb{S}_{Max}$ Variation for One Souslin Tree.Paul Larson - 1999 - Journal of Symbolic Logic 64 (1):81-98.
Gap Structure After Forcing with a Coherent Souslin Tree.Carlos Martinez-Ranero - 2013 - Archive for Mathematical Logic 52 (3-4):435-447.
Souslin Forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.
On Iterating Semiproper Preorders.Tadatoshi Miyamoto - 2002 - Journal of Symbolic Logic 67 (4):1431-1468.
A Microscopic Approach to Souslin-Tree Constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
Creatures on Ω 1 and Weak Diamonds.Heike Mildenberger - 2009 - Journal of Symbolic Logic 74 (1):1-16.
Club Degrees of Rigidity and Almost Kurepa Trees.Gunter Fuchs - 2013 - Archive for Mathematical Logic 52 (1-2):47-66.
Can a Small Forcing Create Kurepa Trees.Renling Jin & Saharon Shelah - 1997 - Annals of Pure and Applied Logic 85 (1):47-68.
Degrees of Rigidity for Souslin Trees.Gunter Fuchs & Joel David Hamkins - 2009 - Journal of Symbolic Logic 74 (2):423-454.
Chain Homogeneous Souslin Algebras.Gido Scharfenberger-Fabian - 2011 - Mathematical Logic Quarterly 57 (6):591-610.
Souslin Algebra Embeddings.Gido Scharfenberger-Fabian - 2011 - Archive for Mathematical Logic 50 (1-2):75-113.

Analytics

Added to PP index
2019-06-11

Total views
7 ( #1,071,872 of 2,519,700 )

Recent downloads (6 months)
1 ( #406,314 of 2,519,700 )

How can I increase my downloads?

Downloads

My notes