Opendata, web and dolomites


Regularity properties, definability and combinatorics on the real line.

Total Cost €


EC-Contrib. €






Project "REGPROP" data sheet

The following table provides information about the project.


Organization address
address: MITTELWEG 177
postcode: 20148
website: n.a.

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 Germany [DE]
 Total cost 171˙460 €
 EC max contribution 171˙460 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2017
 Duration (year-month-day) from 2017-03-01   to  2019-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAET HAMBURG DE (HAMBURG) coordinator 171˙460.00


 Project objective

'This proposed research is in mathematical logic and foundations of mathematics, more specifically in set theory. It is motivated by the interplay between regularity properties and definability for subsets of real numbers. By 'regularity properties' we are referring to certain desirable properties of sets, and by 'definability' to the logical description of such sets, in the sense of Descriptive Set Theory.

The study of such questions goes back to classical issues in topology, analysis and related fields of mathematics, raised by the great pioneers of abstract mathematics of the late 19th and early 20th century, such as Georg Cantor, Emile Borel, Henri Lebesgue and others. These mathematicians were faced with seemingly insurmountable challenges which could only be resolved later with the advent of logical and meta-mathematical methods, developed by Kurt Gödel in 1938 and by Paul Cohen in 1964.

Since that time, the study of Regularity Properties has continued to hold a central position in the foundations of mathematics. Many mathematicians and logicians of high status and prestige have contributed to this area, among them W. Hugh Woodin (winner of the Hausdorff Medal 2013), Stevo Todorčević (winner of the CRM-Fields-PIMS prize 2012) and Saharon Shelah (winner of numerous awards, among them the Erdös Prize 1977 and the Karp Prize 1983).

We propose to contribute to this line of research in a number of interrelated directions, such as: studying new regularity properties (relevant to other fields of mathematics), developing abstract frameworks for such properties, studying higher complexity classes, and generalising results to spaces other than the classical real numbers. Several technical results involving the method of 'forcing' needed to construct models of set theory, will also be worked out along the way.'


year authors and title journal last update
List of publications.
2019 Benedikt Löwe, Robert Passmann, Sourav Tarafer,
Constructing illoyal algebra-valued models of set theory
published pages: , ISSN: , DOI:
Submitted for publication in a peer-reviewed journal 2019-06-06
2018 Yurii Khomskii
Habilitationsschrift: Cardinal Characteristics, Regularity Properties, Definability and the Structure of the Real Line and the Generalised Real Line
published pages: , ISSN: , DOI:
2019 Andrés Eduardo Caicedo, Benedikt Löwe
The fourteen Victoria Delfino problems and their status in the year 2019
published pages: , ISSN: , DOI:
Reissued Cabal volumes, Volume 4, to appear 2019-06-06
2019 Lorenzo Galeotti
The theory of the generalised real numbers and other topics in logic (PhD Thesis)
published pages: , ISSN: , DOI:
ILLC Dissertation Series DS-2019-04 2019-06-06
2018 Jörg Brendle, Vera Fischer, Yurii Khomskii
Definable maximal independent families
published pages: 1, ISSN: 0002-9939, DOI: 10.1090/proc/14497
Proceedings of the American Mathematical Society 2019-06-06
2019 Robert Passmann
The de Jongh property for bounded constructive Zermelo-Fraenkel settheory
published pages: , ISSN: , DOI:
Submitted for publication in a peer-reviewed journal 2019-06-06

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