2016 Fiscal Year Final Research Report
Infinite Ramsey theory and combinatorics on the reals
| Project/Area Number |
25800089
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Shizuoka University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Keywords | 公理的集合論 / 強制法理論 |
|---|
| Outline of Final Research Achievements |
There are several open problems on Ramsey theoretic properties and assertions. For example, the countable chain condition is a representative of Ramsey theoretic properties on the forcing theory, and the following assertions can be considered as Ramsey theoretic assertions: There are no S-spaces, there are no entangled sets of reals, and the P-ideal Dichotomy.
In the project, it is studied that (1) Prikry's problem on ccc forcings, (2) new properties of ideal-based forcings, and (3) the consistency about the existence of a non-special Aronszajn tree with a couple of Ramsey theoretic assertions.
|
| Free Research Field |
公理的集合論
|
