Mathematical, Foundational and Computational Aspects of the Higher Infinite

Mathematical, Foundational and Computational Aspects of the Higher Infinite's image
Created: 2015-08-25 17:16
Institution: Isaac Newton Institute for Mathematical Sciences
Description: The goals of set theory are the analysis of the structure of the Higher Infinite, i.e. Cantor's set-theoretic universe and the elucidation of the nature of infinite mathematical objects and their role in foundational issues underlying mathematics. Moreover, the current standard system of set theory, the Zermelo-Fraenkel axioms with the Axiom of Choice (ZFC), is the usual framework for a large part of mathematics.

Current set-theoretic research on infinity focuses on the following three broad areas: large Cardinals and inner model theory, descriptive set-theoretic methods and classification problems, and infinite combinatorics.

The programme HIF will connect these three main strands of set-theoretic research and other fields of set theory to the wider scope of mathematics, to research in the foundations of mathematics, including some philosophical issues, and to research on computational issues of infinity, e.g. in theoretical computer science and constructive mathematics.

The following topics are a non-exclusive list of important examples of relevant fields for the research done in the programme HIF:
1.The structure of definable subsets of the continuum
2.Infinite combinatorics, forcing, and large cardinals
3.Inner models of large cardinals and aspects of determinacy
4.Applications of set theory to other areas of mathematics
5.Constructive set theory and new models of computation
6.Set theory and the foundations of mathematics

Three workshops are planned during the programme: The first one (24-28 August 2015) will be the 5th European Set Theory Conference. The second workshop, entitled "New challenges in iterated forcing" will be a Satellite Meeting held at the University of East Anglia in Norwich (2-6 November 2015). A final workshop will take place on 14-18 December 2015.
 

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Self-determined sets of sentences

   50 views

Rivello, E (Università degli Studi di Torino)
Wednesday 2nd September 2015 - 14:40 to 15:10

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 6 Oct 2015


Ultrafilters without p-point quotients

   28 views

Goldstern, M (Technische Universität Wien)
Friday 28 August 2015, 10:00-11:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 2 Sep 2015


A generalisation of closed unbounded sets

   41 views

Brickhill, H (University of Bristol)
Monday 24 August 2015, 13:30-14:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 25 Aug 2015


A revision theory for type-free probability

   34 views

Campbell Moore, CJ (Ludwig-Maximilians-Universität München)
Monday 14th December 2015 - 16:00 to 17:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 21 Dec 2015


A super-Dowker filter

   42 views

Cummings, JWR (Carnegie Mellon University)
Thursday 27 August 2015, 16:00-17:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 1 Sep 2015


An Introduction to infinite matroids

   70 views

Carmesin, J (University of Cambridge)
Thursday 17th December 2015 - 13:30 to 14:30

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 23 Dec 2015


Another proof of the Jayne-Rogers theorem

   150 views

Miller, B (Universität Wien)
Friday 18th December 2015 - 10:00 to 11:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 23 Dec 2015


Approximate Ramsey properties of Matrices

   30 views

Lopez-Abad, J (Consejo Superior de Investigaciones Cientificas)
Monday 14th December 2015 - 13:30 to 14:30

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 21 Dec 2015


Around the definability of mad families

   35 views

Törnquist, A D (Københavns Universitet)
Monday 24 August 2015, 15:00-16:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 25 Aug 2015


Aspects of generalizing the concept of strong measure zero

   33 views

Wohofsky, W (Technische Universität Wien)
Tuesday 29th September 2015 - 16:00 to 17:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 6 Oct 2015


Borel Matchings and equidecompositions

   74 views

Marks, A [CALTECH (California Institute of Technology)]
Friday 18th December 2015 - 11:30 to 12:30

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 23 Dec 2015


Cofinalities of Marczewski Ideals

   29 views

Khomskii, Y (Universität Hamburg)
Wednesday 26 August 2015, 13:30-14:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 1 Sep 2015


Computable analysis and games in descriptive set theory

   31 views

Nobrega, H (Universiteit van Amsterdam)
Friday 9th October 2015 - 12:30 to 13:25

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 16 Oct 2015


Connecting topological dimension theory and recursion theory

   39 views

Pauly, A (University of Cambridge)
Thursday 27 August 2015, 13:30-14:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 28 Sep 2015


Consecutively large families below the first inaccessible cardinal

   29 views

Brech, C (Universidade de São Paulo)
Thursday 29th October 2015 - 16:00 to 17:00

Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 4 Nov 2015


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