HIF
19 August 2015 to 18 December 2015
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:
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.
Another UK event closely related to the HIF topics are the LMS Invited Lectures 2014 given by Jouko Väänänen at UEA, April 14-17, 2014.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Mathematical, foundational and computational aspects of the higher infinite, where work on this paper was undertaken. This work was supported by EPSRC grant EP/K032208/1.
Click here to download the programme's final scientific report
Title | Year | Programme | Publication Date |
---|---|---|---|
Dependent choice, properness, and generic absolutenessAuthors: David Aspero, Asaf Karagila |
2015 | HIF | 13 June 2018 |
THE UNIVERSAL HOMOGENEOUS TRIANGLE-FREE GRAPH HAS FINITE BIG RAMSEY DEGREESAuthors: N. Dobrinen |
2015 | HIF | 2 October 2017 |
Towards computable analysis on the generalised real lineAuthors: Lorenzo Galeotti, Hugo Nobrega |
2015 | HIF | 19 April 2017 |
Cofinalities of Marczewski-like idealsAuthors: Dr Yurii Khomskii (Hamburg University), Dr Wolfgang Wohofskyy (Hamburg University), Prof. Jörg Bendle (Graduate School of System Informatics Kobe University) |
2015 | HIF | 2 March 2017 |
Filter-Laver MeasurabilityAuthors: Dr Yuri Khomskii (Universität Hamburg) |
2015 | HIF | 2 March 2017 |
The rearrangement numberAuthors: Professor Jörg Brendle, Dr Will Brian, Joel David Hamkins, et al., Professor Andreas Blass |
2015 | HIF | 2 March 2017 |
Cofinalities of Marczewski-like idealsAuthors: Wolfgang Wohofsky, Jörg Brendle, Yurii Khomskii |
2015 | HIF | 2 March 2017 |
Game characterizations and lower cones in the Weihrauch degreesAuthors: H Nobrega, A Pauly |
2015 | HIF | 21 October 2016 |
Measures on Suslinean spacesAuthors: P Borodulin-nadzieja, G Plebanek |
2015 | HIF | 21 October 2016 |
A multiplication operation for the hierachy of normsAuthors: AC Block, B Lowe |
2015 | HIF | 21 October 2016 |
Normal measures and strongly compact cardinalsAuthors: AW Apter |
2015 | HIF | 21 October 2016 |
Forcing the truth of a weak form of Schanuel's conjectureAuthors: M Viale |
2015 | HIF | 21 October 2016 |
$\it C$*-algebras and B-names for complex numbersAuthors: A Vaccaro, M Viale |
2015 | HIF | 21 October 2016 |
The minimal size of infinite maximal antichains in direct products of partial ordersAuthors: MS Kurilic |
2015 | HIF | 21 October 2016 |
Recognizable sets and Woodin cardinals: computation beyond the constructible universeAuthors: M Carl, P Schlicht, P Welch |
2015 | HIF | 21 October 2016 |
Inner models from extended logicsAuthors: J Kennedy, M Magidor, J Vaananen |
2015 | HIF | 21 October 2016 |
On properties of compacta that do not reflect in small continuous imagesAuthors: M Magidor, G Plebanek |
2015 | HIF | 21 October 2016 |
Seperating the fan theorem and its weakenings IIAuthors: RS Lubarsky |
2015 | HIF | 21 October 2016 |
Philosophy or not? The study of cultures and practices of mathematicsAuthors: B Lowe |
2015 | HIF | 21 October 2016 |
A candidate for the generalised real lineAuthors: L Galeotti |
2015 | HIF | 21 October 2016 |
Restrictiveness relative to notions of interpretationAuthors: L Incurvati, B Lowe |
2015 | HIF | 21 October 2016 |
The quandry of quandles: The Borel completeness of a knot invariantAuthors: AD Brooke-taylor, SK Miller |
2015 | HIF | 21 October 2016 |
Ascending paths and forcings that specialize higher Aronszajn treesAuthors: P Lucke |
2015 | HIF | 21 October 2016 |
The $\kappa$$^+$-antichain property for ($\kappa$,1)-simplified morassesAuthors: C Morgan |
2015 | HIF | 21 October 2016 |
$\Sigma$$_1$($\kappa$)-Definable subsets of H($\kappa$$^+$)Authors: P Lucke, R Schindler, P Schlicht |
2015 | HIF | 21 October 2016 |
Diagnonalising an ultrafilter and preserving a $\rho$-pointAuthors: H Mildenberger |
2015 | HIF | 21 October 2016 |
The higher sharp IAuthors: Y Zhu |
2015 | HIF | 21 October 2016 |
Exact completetion of path categories and algebraic set theoryAuthors: B Van Den Berg, I Meordijk |
2015 | HIF | 21 October 2016 |
Measures and fibersAuthors: P Borodulin-nadzieja |
2015 | HIF | 21 October 2016 |
Measures and slalomsAuthors: P Borodulin-nadzieja, T Inamdar |
2015 | HIF | 21 October 2016 |
Singularizing successor cardinals by forcingAuthors: D Adolf, AW Apter, P Koepke |
2015 | HIF | 21 October 2016 |
The Haplern-Läuchli theorem at a measurable cardinalAuthors: N Dobrinen, D Hathaway |
2015 | HIF | 21 October 2016 |
Derived topologies on ordinals and stationary reflectionAuthors: Joan Bagaria |
2015 | HIF | 21 October 2016 |
Mathias and set theoryAuthors: A Kanamori |
2015 | HIF | 21 October 2016 |
Homogeneous families on trees and subsymmetric basic sequencesAuthors: C Brech, J Lopez-Abad, S Todorcevic |
2015 | HIF | 21 October 2016 |
Power Kripke-Platek set theory and the axiom of choiceAuthors: Michael Rathjen |
2015 | HIF | 21 October 2016 |
Generic Vopěnka's principle, remarkable cardinals, and the weak proper forcing axiomAuthors: Joan Bagaria, Dr Victoria Gitman (The City University of New York), Prof. Ralf Schindler (Institut für mathematische Logik und Grundlagenforschung) |
2015 | HIF | 21 October 2016 |
The modal logic of inner modelsAuthors: T Inamdar, B Lowe |
2015 | HIF | 21 October 2016 |
Partitions and conservativityAuthors: A Blass |
2015 | HIF | 21 October 2016 |
Almost disjoin refinements and mixing realsAuthors: B Farkas, Y Khomskii, Z Vidnyanszky |
2015 | HIF | 21 October 2016 |
Creature forcing and topological Ramsey spacesAuthors: N Dobrinen |
2015 | HIF | 21 October 2016 |
Infinite dimensional Ellentuck spaces and Ramsey-classification theoremsAuthors: N Dobrinen |
2015 | HIF | 21 October 2016 |
G$\delta$$\sigma$-games and generalized computationAuthors: PD Welch |
2015 | HIF | 21 October 2016 |
Obtaining Woodin's cardinalsAuthors: PD Welch |
2015 | HIF | 21 October 2016 |
On hidden variables: value and expectation no-go theoremsAuthors: A Blass, Y Gurevich |
2015 | HIF | 21 October 2016 |
Open determinacy for class gamesAuthors: V Gitman, JD Hamkins |
2015 | HIF | 21 October 2016 |
A position in infinite chess with game value $\omega$$^4$Authors: CDA Evans, JD Hamkins, NL Perlmutter |
2015 | HIF | 21 October 2016 |
Upward closure and amalgamation in the generic multiverse of a countable model of set theoryAuthors: JD Hamkins |
2015 | HIF | 21 October 2016 |
24 August 2015 to 28 August 2015
14 December 2015 to 18 December 2015
Tuesday 1st September 2015 | |||
---|---|---|---|
13:00 to 14:00 | Room 1 | ||
14:00 to 15:00 | Room 1 | ||
15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 |
Models of Intuitionistic Zermelo-Frankel Set Theory based on Scott's $D_{\infty}$ |
Room 1 | |
16:30 to 17:30 | Room 1 |
Wednesday 2nd September 2015 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | ||
13:30 to 14:40 |
Weak Partition Relations and Conservative Elementary Extensions |
Room 1 | |
14:40 to 15:10 | Room 2 | ||
14:40 to 15:10 | Room 1 | ||
15:10 to 15:40 | Room 2 | ||
15:10 to 15:40 | Room 1 | ||
15:40 to 16:00 | No Room Required | ||
16:00 to 17:00 | Room 1 | ||
17:00 to 18:00 | No Room Required |
Thursday 3rd September 2015 | |||
---|---|---|---|
09:00 to 10:00 | Room 1 | ||
09:00 to 17:00 | Room 2 | ||
09:00 to 19:00 | Room 1 | ||
10:00 to 11:00 | Room 1 | ||
11:00 to 11:20 | No Room Required | ||
11:20 to 12:20 | Room 1 | ||
12:20 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:40 to 15:10 |
On a Generalization of the Revision-theoretic Approach to Strategic Rationality |
Room 1 | |
15:10 to 15:40 | Room 1 | ||
15:10 to 15:40 |
Partition Relation for linear Orders without the Axiom of Choice |
Room 2 | |
15:40 to 16:00 | No Room Required | ||
16:00 to 17:00 | Room 1 | ||
17:15 to 18:15 | Room 1 | ||
19:00 to 19:30 | No Room Required |
Friday 4th September 2015 | |||
---|---|---|---|
09:00 to 15:00 | Room 1 | ||
09:00 to 10:00 | Room 1 | ||
09:00 to 17:00 | Discussion Room | ||
10:10 to 10:40 | Room 1 | ||
10:10 to 10:40 | Room 2 | ||
10:40 to 11:10 | Room 1 | ||
10:40 to 11:10 | Room 2 | ||
11:10 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | ||
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 |
Tuesday 8th September 2015 | |||
---|---|---|---|
15:00 to 16:00 | Room 2 |
Thursday 1st October 2015 | |||
---|---|---|---|
15:00 to 16:00 | Room 2 |
Monday 5th October 2015 | |||
---|---|---|---|
16:00 to 17:00 |
Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture |
Room 1 |
Friday 9th October 2015 | |||
---|---|---|---|
12:30 to 13:25 | Room 2 | ||
13:30 to 14:25 | Room 2 | ||
14:40 to 15:35 | Room 2 | ||
15:50 to 16:45 |
Uncountably many maximal-closed subgroups of Sym(N) via reducts of Henson digraphs |
Room 2 |
Saturday 10th October 2015 | |||
---|---|---|---|
11:00 to 11:55 | Room 1 | ||
13:00 to 13:55 | Room 1 | ||
14:00 to 14:55 | Room 1 |
Thursday 29th October 2015 | |||
---|---|---|---|
15:00 to 16:00 |
Approximate Ramsey properties of matrices and finite dimensional normed spaces |
Room 2 | |
16:00 to 17:00 |
Consecutively large families below the first inaccessible cardinal |
Room 2 |
Tuesday 10th November 2015 | |||
---|---|---|---|
15:00 to 16:00 |
On two problems on Boolean algebras and finitely additive measures |
Room 2 |
Tuesday 17th November 2015 | |||
---|---|---|---|
15:00 to 16:00 |
Reflection numbers of some combinatorial and topological properties |
Room 2 |
Tuesday 1st December 2015 | |||
---|---|---|---|
15:00 to 16:00 | Room 2 |
Tuesday 8th December 2015 | |||
---|---|---|---|
15:00 to 16:00 | Room 2 |
Thursday 10th December 2015 | |||
---|---|---|---|
15:00 to 16:00 |
Some more on $G_\delta\sigma$ determinacy and generalized recursion |
Room 2 |
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