Piece selection and cardinal arithmetic

Mathematical Logic Quarterly 68 (4):416-446 (2022)
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Abstract

We study the effects of piece selection principles on cardinal arithmetic (Shelah style). As an application, we discuss questions of Abe and Usuba. In particular, we show that if, then (a) is not (λ, 2)‐distributive, and (b) does not hold.

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10.1002/malq.202100033

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References found in this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
The strenght of the failure of the singular cardinal hypothesis.Moti Gitik - 1991 - Annals of Pure and Applied Logic 51 (3):215-240.
The combinatorial essence of supercompactness.Christoph Weiß - 2012 - Annals of Pure and Applied Logic 163 (11):1710-1717.

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