Abstract
In this series of papers we advance Ramsey theory over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions that homogenize colorings over them is uncovered. At the level of the first uncountable cardinal this gives rise to a duality theorem under Martin’s Axiom: a function p: [ω1]2 → ω witnesses a weak negative Ramsey relation when p plays the role of a coloring if and only if a positive Ramsey relation holds over p when p plays the role of a partition. The consistency of positive Ramsey relations over partitions does not stop at the first uncountable cardinal: it is established that at arbitrarily high uncountable cardinals these relations follow from forcing axioms without large cardinal strength. This result solves in particular two problems from [CKS21].
Original language | English |
---|---|
Pages (from-to) | 205-222 |
Number of pages | 18 |
Journal | Israel Journal of Mathematics |
Volume | 261 |
Issue number | 1 |
DOIs | |
State | Published - Jun 2024 |
Bibliographical note
Publisher Copyright:© The Hebrew University of Jerusalem 2023.
Funding
Kojman was partially supported by the Israel Science Foundation (grant agreement 665/20). Rinot was partially supported by the Israel Science Foundation (grant agreement 2066/18) and by the European Research Council (grant agreement ERC-2018-StG 802756). Steprāns was partially supported by NSERC of Canada.
Funders | Funder number |
---|---|
Natural Sciences and Engineering Research Council of Canada | |
European Commission | ERC-2018-StG 802756 |
Israel Science Foundation | 2066/18, 665/20 |