Combinatorics and compactness at small uncountable cardinals
Public support
Provider
Czech Science Foundation
Programme
Standard projects
Call for proposals
SGA0202600001
Main participants
Matematický ústav AV ČR, v. v. i.
Contest type
VS - Public tender
Contract ID
26-22502S
Alternative language
Project name in Czech
Combinatorics and compactness at small uncountable cardinals
Annotation in Czech
The proposed project will investigate questions in combinatorial set theory, focusing in particular on combinatorics at the first two uncountable cardinals, which are of primary importance in applications of set theory to other fields of mathematics, particularly those centrally involving the real numbers. We plan to focus in particular on higher descriptive set theory at the first uncountable cardinal and compactness phenomena, regarding the extent to which global properties of structures are determined by their local properties, at the second uncountable cardinal. We will address prominent open questions in these areas, including problems on the reflection of metrizability of topological spaces, combinatorial consequences of forcing axioms, and connections with singular cardinals that lie at the heart of deep questions in cardinal arithmetic.
Scientific branches
R&D category
ZV - Basic research
OECD FORD - main branch
10101 - Pure mathematics
OECD FORD - secondary branch
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OECD FORD - another secondary branch
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CEP - equivalent branches <br>(according to the <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">converter</a>)
BA - General mathematics
Solution timeline
Realization period - beginning
Jan 1, 2026
Realization period - end
Dec 31, 2028
Project status
Z - Beginning multi-year project
Latest support payment
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Data delivery to CEP
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data delivery code
CEP26-GA0-GA-R
Data delivery date
May 4, 2026
Finance
Total approved costs
10,156 thou. CZK
Public financial support
10,036 thou. CZK
Other public sources
120 thou. CZK
Non public and foreign sources
0 thou. CZK