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SAIFIA SIGNED

Strong Axioms of Infinity: Frameworks, Interactions and Applications

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EC-Contrib. €

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Project "SAIFIA" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAT DE BARCELONA 

Organization address
address: GRAN VIA DE LES CORTS CATALANES 585
city: BARCELONA
postcode: 8007
website: http://www.ub.es

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Spain [ES]
 Total cost 172˙932 €
 EC max contribution 172˙932 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2018
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2020
 Duration (year-month-day) from 2020-04-01   to  2022-03-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT DE BARCELONA ES (BARCELONA) coordinator 172˙932.00

Map

 Project objective

In spite of their central role in modern set theory, strong axioms of infinity (or large cardinal axioms) are still surrounded by an aura of vagueness, a lack of generality and many open conceptual questions. After the study of large cardinals has evolved for over eighty years, recent results suggest that it now makes sense to develop a general theory of strong axioms of infinity in which all known large cardinals are seen as milestones in a hierarchy of mathematical principles derived from some much more general considerations about the reflective properties of the set-theoretic universe. The development of such a theory would lead to a breakthrough in our understanding of large cardinals and their role in mathematics, and provide strong justifications for their acceptance as true mathematical statements. In this project, we want to work towards this breakthrough with the help of novel combinations of concepts and techniques from different areas of set theory.

We will develop general frameworks for strong axioms of infinity that incorporate all types of large cardinals studied so far. The work of the proposed supervisor on structural reflection properties and recent pioneering results in combinatorial set theory will serve as the starting points for this work.

Moreover, motivated by the strong influence of large cardinals on the theory of definable sets of real numbers, we will study the impact of these axioms on definability at higher cardinalities. This task is closely related to one of the most important developments in modern set theory, Hugh Woodin’s programme of constructing a canonical inner model containing a supercompact cardinal.

Finally, strong axioms of infinity have recently been used with great success to answer questions in other branches of mathematics, like category theory or homotopy theory. These results opened up a wide area of possible applications of set-theoretic results that we also want to explore in our project.

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The information about "SAIFIA" are provided by the European Opendata Portal: CORDIS opendata.

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