# Mathematical, Foundational and Computational Aspects of the Higher Infinite

Created: | 2015-08-25 17:16 |
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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