Weak prediction principles

Omer Ben-Neria; Shimon Garti; Yair Hayut

doi:https://doi.org/10.4064/fm576-6-2018

Weak prediction principles

Omer Ben-Neria, Shimon Garti, Yair Hayut

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We prove the consistency of the failure of the weak diamond Φ _λ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψ _λ is equivalent to the statement 2 ^<λ < 2 ^λ and hence holds at every strongly inaccessible cardinal.

Original language	English
Pages (from-to)	109-125
Number of pages	17
Journal	Fundamenta Mathematicae
Volume	245
Issue number	2
DOIs	https://doi.org/10.4064/fm576-6-2018
State	Published - 2019

Keywords

Radin forcing
Very weak diamond
Weak diamond

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.4064/fm576-6-2018

Cite this

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title = "Weak prediction principles",

abstract = " We prove the consistency of the failure of the weak diamond Φ λ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψ λ is equivalent to the statement 2 <λ < 2 λ and hence holds at every strongly inaccessible cardinal.",

keywords = "Radin forcing, Very weak diamond, Weak diamond",

author = "Omer Ben-Neria and Shimon Garti and Yair Hayut",

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AU - Ben-Neria, Omer

AU - Garti, Shimon

AU - Hayut, Yair

N1 - Publisher Copyright: © Instytut Matematyczny PAN

PY - 2019

Y1 - 2019

N2 - We prove the consistency of the failure of the weak diamond Φ λ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψ λ is equivalent to the statement 2 <λ < 2 λ and hence holds at every strongly inaccessible cardinal.

AB - We prove the consistency of the failure of the weak diamond Φ λ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond Ψ λ is equivalent to the statement 2 <λ < 2 λ and hence holds at every strongly inaccessible cardinal.

KW - Radin forcing

KW - Very weak diamond

KW - Weak diamond

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U2 - https://doi.org/10.4064/fm576-6-2018

DO - https://doi.org/10.4064/fm576-6-2018

M3 - Article

SN - 0016-2736

VL - 245

SP - 109

EP - 125

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 2

ER -

Weak prediction principles

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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