BeyondA1 SIGNED
Set theory beyond the first uncountable cardinal
Total Cost €
0EC-Contrib. €
0Partnership
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0BeyondA1 project word cloud
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Project "BeyondA1" data sheet
The following table provides information about the project.
| Coordinator |
BAR ILAN UNIVERSITY
Organization address contact info |
| Coordinator Country | Israel [IL] |
| Total cost | 1˙362˙500 € |
| EC max contribution | 1˙362˙500 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2018-STG |
| Funding Scheme | ERC-STG |
| Starting year | 2018 |
| Duration (year-month-day) | from 2018-10-01 to 2023-09-30 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | BAR ILAN UNIVERSITY | IL (RAMAT GAN) | coordinator | 1˙362˙500.00 |
Map
Project objective
We propose to establish a research group that will unveil the combinatorial nature of the second uncountable cardinal. This includes its Ramsey-theoretic, order-theoretic, graph-theoretic and topological features. Among others, we will be directly addressing fundamental problems due to Erdos, Rado, Galvin, and Shelah. While some of these problems are old and well-known, an unexpected series of breakthroughs from the last three years suggest that now is a promising point in time to carry out such a project. Indeed, through a short period, four previously unattainable problems concerning the second uncountable cardinal were successfully tackled: Aspero on a club-guessing problem of Shelah, Krueger on the club-isomorphism problem for Aronszajn trees, Neeman on the isomorphism problem for dense sets of reals, and the PI on the Souslin problem. Each of these results was obtained through the development of a completely new technical framework, and these frameworks could now pave the way for the solution of some major open questions. A goal of the highest risk in this project is the discovery of a consistent (possibly, parameterized) forcing axiom that will (preferably, simultaneously) provide structure theorems for stationary sets, linearly ordered sets, trees, graphs, and partition relations, as well as the refutation of various forms of club-guessing principles, all at the level of the second uncountable cardinal. In comparison, at the level of the first uncountable cardinal, a forcing axiom due to Foreman, Magidor and Shelah achieves exactly that. To approach our goals, the proposed project is divided into four core areas: Uncountable trees, Ramsey theory on ordinals, Club-guessing principles, and Forcing Axioms. There is a rich bilateral interaction between any pair of the four different cores, but the proposed division will allow an efficient allocation of manpower, and will increase the chances of parallel success.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2019 |
Ari Meir Brodsky, Assaf Rinot A Remark on Schimmerling’s Question published pages: 525-561, ISSN: 0167-8094, DOI: 10.1007/s11083-019-09482-7 |
Order 36/3 | 2020-03-23 |
| 2019 |
Assaf Rinot Souslin trees at successors of regular cardinals published pages: 200-204, ISSN: 0942-5616, DOI: 10.1002/malq.201800065 |
Mathematical Logic Quarterly 65/2 | 2020-03-23 |
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