More notions of forcing add a souslin tree

Ari Meir Brodsky; Assaf Rinot

doi:10.1215/00294527-2019-0011

More notions of forcing add a souslin tree

Ari Meir Brodsky, Assaf Rinot

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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	https://doi.org/10.1215/00294527-2019-0011
State	Published - 1 Jan 2019
Externally published	Yes

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

ASJC Scopus subject areas

Logic

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10.1215/00294527-2019-0011

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title = "More notions of forcing add a souslin tree",

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.",

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AU - Rinot, Assaf

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AB - 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.

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KW - Hechler forcing

KW - Magidor forcing

KW - Microscopic approach

KW - Outside guessing of clubs

KW - Parameterized proxy principle

KW - Prikry forcing

KW - Radin forcing

KW - Souslin-tree construction

KW - square principle

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More notions of forcing add a souslin tree

Abstract

Keywords

ASJC Scopus subject areas

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