2024/10/08 by Tom Benhamou, Benhamou, Tom · 3 citations
Energy · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Heat Transfer and Optimization #Logic (math.LO) #Solar-Powered Water Purification Methods
paper · pdf · doi:10.48550/arxiv.2410.06275
openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the Tukey order, the Galvin property/ Cohesive ultrafilters from \citeKanamori1978 in terms of ultrapowers. We use this characterization to measure the distance between the Tukey order and other well-known orders of ultrafilters. Secondly, we improve two theorems of Kanamori \citeKanamori1978 from the 70's. We then study the point spectrum and the depth spectrum of an ultrafilter, and give a simple positive answer to Kanamori's question \cite[Question 2]Kanamori1978 starting from a supercompact cardinal. We also prove that a positive answer requires more than o(κ)=κ++. Finally, we prove several consistency results regarding the point and depth spectrum.