Double weakness

S. Garti; S. Shelah

doi:https://doi.org/10.1007/s10474-021-01132-y

Double weakness

S. Garti, S. Shelah

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 ^θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.

Original language	English
Pages (from-to)	379-391
Number of pages	13
Journal	Acta Mathematica Hungarica
Volume	163
Issue number	2
DOIs	https://doi.org/10.1007/s10474-021-01132-y
State	Published - Apr 2021

Keywords

Cohen forcing
Radin forcing
very weak diamond
weak diamond
weakly inaccessible

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1007/s10474-021-01132-y

Cite this

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title = "Double weakness",

abstract = "We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.",

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T1 - Double weakness

AU - Garti, S.

AU - Shelah, S.

PY - 2021/4

Y1 - 2021/4

N2 - We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.

AB - We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.

KW - Cohen forcing

KW - Radin forcing

KW - very weak diamond

KW - weak diamond

KW - weakly inaccessible

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U2 - https://doi.org/10.1007/s10474-021-01132-y

DO - https://doi.org/10.1007/s10474-021-01132-y

M3 - مقالة

SN - 0236-5294

VL - 163

SP - 379

EP - 391

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 2

ER -

Double weakness

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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