Abstract
We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets.
| Original language | English |
|---|---|
| Pages (from-to) | 855-870 |
| Number of pages | 16 |
| Journal | Journal of Symbolic Logic |
| Volume | 86 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jun 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021, Association for Symbolic Logic
Funding
Acknowledgments. The first author was partially supported by NSF of China grants 11801386 and 11771311. The second author was partially supported by PAPIIT grants IN 100317 and IN 104220, and a CONACyT grant A1-S-16164. The fourth author was partially supported by NSF grant DMS-1954069.
| Funders | Funder number |
|---|---|
| PAPIIT | IN 104220, IN 100317 |
| National Science Foundation | DMS-1954069 |
| National Natural Science Foundation of China | 11771311, 11801386 |
| Consejo Nacional de Ciencia y Tecnología | A1-S-16164 |
Keywords
- F ideal
- Tukey order
- flat ideal
- gradually flat ideal