Mathematical, Foundational and Computational Aspects of the Higher Infinite

by Cambridge University

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 continuum2.Infinite combinatorics, forcing, and large cardinals3.Inner models of large cardinals and aspects of determinacy4.Applications of set theory to other areas of mathematics5.Constructive set theory and new models of computation6.Set theory and the foundations of mathematicsThree 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.

More
Recent Episodes
  • Self-determined sets of sentences
    Oct 6, 2015 – 27:12
  • Ultrafilters without p-point quotients
    Sep 2, 2015 – 55:54
  • 101 Years of Modern Set Theory: Felix Hausdorff's "Foundations of Set Theory"
    Aug 25, 2015 – 58:34
  • A generalisation of closed unbounded sets
    Aug 25, 2015 – 26:26
  • A revision theory for type-free probability
    Dec 21, 2015 – 01:03:00
  • A super-Dowker filter
    Sep 1, 2015 – 59:25
  • An Introduction to infinite matroids
    Dec 23, 2015 – 57:28
  • Another proof of the Jayne-Rogers theorem
    Dec 23, 2015 – 01:02:00
  • Approximate Ramsey properties of Matrices
    Dec 21, 2015 – 58:30
  • Approximate Ramsey properties of matrices and finite dimensional normed spaces
    Nov 4, 2015 – 56:25
  • Around the definability of mad families
    Aug 25, 2015 – 56:25
  • Aspects of generalizing the concept of strong measure zero
    Oct 6, 2015 – 01:09:00
  • Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture
    Oct 8, 2015 – 01:01:00
  • Borel Matchings and equidecompositions
    Dec 23, 2015 – 59:07
  • Chain conditions, layered partial orders and weak compactness
    Sep 1, 2015 – 28:19
  • Cofinalities of Marczewski Ideals
    Sep 1, 2015 – 26:44
  • Computable analysis and games in descriptive set theory
    Oct 16, 2015 – 44:06
  • Computing beyond Constructibility: The Recognizability Strength of Ordinal Time Machines
    Dec 21, 2015 – 57:43
  • Connecting topological dimension theory and recursion theory
    Sep 28, 2015 – 31:46
  • Consecutively large families below the first inaccessible cardinal
    Nov 4, 2015 – 54:52
  • Context-Dependent Deterministic Parallel Feedback Turing Computability
    Dec 23, 2015 – 01:01:00
  • Conway's funniest talk ever
    Nov 25, 2015 – 01:04:00
  • Delta_1-definability of the non-stationary ideal
    Sep 2, 2015 – 47:10
  • Determinacy in Infinite Matroids
    Dec 23, 2015 – 54:26
  • Dual Ramsey theory on trees
    Nov 4, 2015 – 55:39
  • Failures of the Forcing Theorem
    Sep 1, 2015 – 55:16
  • Forcing, regularity properties and the axiom of choice
    Sep 1, 2015 – 19:12
  • Generic I0 at ℵω
    Sep 1, 2015 – 23:52
  • Genius at Play: Reading, Talk, Q&A with John Horton Conway and Siobhan Roberts
    Nov 25, 2015 – 01:46:00
  • Happy Families and Their Relatives
    Sep 1, 2015 – 54:51
  • Hyperclass Forcing in Morse Kelley Set Theory
    Sep 1, 2015 – 29:06
  • Inaccessible cardinals and accessible categories
    Dec 21, 2015 – 58:31
  • Indestructible remarkable cardinals
    Sep 2, 2015 – 59:35
  • Infinite dimensional Ellentuck spaces
    Sep 2, 2015 – 01:00:00
  • Infinite Matroids and Pushdown Automata on Infinite Words
    Dec 21, 2015 – 31:31
  • Linking set theory to economics
    Oct 6, 2015 – 51:43
  • Local Ramsey Theory in abstract spaces
    Sep 1, 2015 – 53:48
  • Long and short recursive constructions---cardinal invariants and parametrized diamonds
    Dec 21, 2015 – 55:22
  • Mathias and Set Theory
    Sep 1, 2015 – 01:00:00
  • On ideal equal convergence
    Sep 2, 2015 – 31:13
  • On relating strong type theories and set theories
    Dec 21, 2015 – 01:06:00
  • On the class of perfectly null sets and its transitive version
    Sep 1, 2015 – 27:17
  • On the width of wqos
    Oct 6, 2015 – 53:01
  • On two problems on Boolean algebras and finitely additive measures
    Nov 23, 2015 – 58:24
  • Order types of chains of Borel sets and Baire functions
    Nov 4, 2015 – 59:39
  • Pairwise Sums in the Reals
    Dec 23, 2015 – 50:46
  • Partition Relation Equiconsistent with ∃κ(o(κ)=κ+)
    Sep 1, 2015 – 32:53
  • Partition Relation Perspectives
    Dec 21, 2015 – 42:41
  • Prikry type sequences: a composition of interconnected results
    Sep 1, 2015 – 59:22
  • Ramsey Determinacy of adversarial Gowers games
    Nov 4, 2015 – 01:00:00
Recent Reviews
Similar Podcasts
Disclaimer: The podcast and artwork on this page are property of the podcast owner, and not endorsed by UP.audio.