Mathematical, Foundational and Computational Aspects of the Higher Infinite
| Created: | 2015-08-25 17:16 |
|---|---|
| Institution: | Isaac Newton Institute for Mathematical Sciences |
| Editors' group: | SMS Editors group for the Newton Institute |
| 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. |
Media items
This collection contains 76 media items.
Media items
Self-determined sets of sentences
95 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
57 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
101 Years of Modern Set Theory: Felix Hausdorff's "Foundations of Set Theory"
319 views
Koepke, P (Universität Bonn)
Monday 24 August 2015, 10:00-11:00
Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 25 Aug 2015
A generalisation of closed unbounded sets
152 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
101 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
92 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
234 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
362 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
90 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
Approximate Ramsey properties of matrices and finite dimensional normed spaces
59 views
Lopez-Abad, J (ICMAT, Madrid)
Thursday 29th October 2015 - 15:00 to 16:00
Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 4 Nov 2015
Around the definability of mad families
64 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
64 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
Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture
172 views
Woodin, H (Harvard University)
Monday 5th 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: Thu 8 Oct 2015
Borel Matchings and equidecompositions
335 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
Chain conditions, layered partial orders and weak compactness
60 views
Lücke, PM (Universität Bonn)
Thursday 27 August 2015, 14:00-14:30
Collection: Mathematical, Foundational and Computational Aspects of the Higher Infinite
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 1 Sep 2015
Cofinalities of Marczewski Ideals
65 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
76 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
Computing beyond Constructibility: The Recognizability Strength of Ordinal Time Machines
255 views
Carl, M (Universität Konstanz)
Wednesday 16th 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
Connecting topological dimension theory and recursion theory
71 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
60 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