A NEW MODEL FOR ALL C-SEQUENCES ARE TRIVIAL

Assaf Rinot; Zhixing You; Jiachen Yuan

doi:10.1017/jsl.2026.10183

A NEW MODEL FOR ALL C-SEQUENCES ARE TRIVIAL

Assaf Rinot
, Zhixing You
, Jiachen Yuan

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

Abstract

We construct a model in which all ℂ-sequences are trivial, yet there exists a Ķ-Souslin tree all of whose limit levels are vanishing levels. This provides an optimal combination of compactness and incompactness. It is obtained by incorporating a so-called mutually exclusive ascent path to Kunen’s 1978 forcing construction, and by analyzing a gallery of Ķ-cc forcing extensions of the outcome model.

Original language	English
Journal	Journal of Symbolic Logic
DOIs	https://doi.org/10.1017/jsl.2026.10183
State	Accepted/In press - 1 Jan 2026
Externally published	Yes

Keywords

Souslin tree
intersection model
mutually exclusive ascent path
vanishing levels
Ķ-chain condition
ℂ-sequence number

ASJC Scopus subject areas

Philosophy
Logic

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10.1017/jsl.2026.10183

Cite this

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abstract = "We construct a model in which all ℂ-sequences are trivial, yet there exists a Ķ-Souslin tree all of whose limit levels are vanishing levels. This provides an optimal combination of compactness and incompactness. It is obtained by incorporating a so-called mutually exclusive ascent path to Kunen{\textquoteright}s 1978 forcing construction, and by analyzing a gallery of Ķ-cc forcing extensions of the outcome model.",

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AB - We construct a model in which all ℂ-sequences are trivial, yet there exists a Ķ-Souslin tree all of whose limit levels are vanishing levels. This provides an optimal combination of compactness and incompactness. It is obtained by incorporating a so-called mutually exclusive ascent path to Kunen’s 1978 forcing construction, and by analyzing a gallery of Ķ-cc forcing extensions of the outcome model.

KW - Souslin tree

KW - intersection model

KW - mutually exclusive ascent path

KW - vanishing levels

KW - Ķ-chain condition

KW - ℂ-sequence number

UR - https://www.scopus.com/pages/publications/105028921083

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JF - Journal of Symbolic Logic

ER -

A NEW MODEL FOR ALL C-SEQUENCES ARE TRIVIAL

Abstract

Keywords

ASJC Scopus subject areas

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