Toronto Set Theory Seminar - Year 2006.

Toronto Set Theory Seminar Year 2007
  1. Friday December 15, 1:30-3:00 Fields Institute, Room 210
    Frank Tall, University of Toronto. Forcing with coherent Souslin trees (continued)
    Abstract: We shall continue developing the technology for forcing with coherent Souslin trees.
  2. Friday December 8, 1:30-3:00 Fields Institute, Room 210
    Frank Tall, University of Toronto. Forcing with coherent Souslin trees (continued)
    Abstract: We shall continue developing the technology for forcing with coherent Souslin trees.
  3. Friday December 1, 1:30-3:00 Fields Institute, Room 210
    Frank Tall, University of Toronto. Forcing with coherent Souslin trees
    Abstract: We shall start developing the technology for forcing with coherent Souslin trees. This lecture will be independent of previous ones on PFA(S)[S].
  4. Friday November 24, 1:30-3:00 Fields Institute, Room 210
    Bernhard Koenig, University of Toronto
    Forcing axioms and their fragments (continued).
  5. Friday November 17, 1:30-3:00 Fields Institute, Room 210
    Frank Tall, University of Toronto. Applications of PFA(S)[S] (continued)
    Abstract: We continue setting up the machinery we started last time, for applications proving collectionwise Hausdorffness.
  6. Friday November 10, 1:30-3:00 Fields Institute, Room 210
    Bernhard Koenig, University of Toronto
    Forcing axioms and their fragments.
    Abstract: We talk about fragments of the forcing axioms PFA or MM, e.g. PFA for posets not adding reals or MM for forcings with the covering property. The theorems we present give a good overview of the strengths of these fragments. Many results are of the following form: start with a model of MM and add an object of size aleph_2 generically; this might destroy the full forcing axiom but very often the extension is mild enough to preserve a fragment of the forcing axiom.
  7. Friday November 3, 1:30-3:00 Fields Institute, Room 210
    Asger Tornquist, University of Toronto
    Non-classification Theorems for conjugacy and orbit equivalence of measure preserving ergodic actions, Part IV.
  8. Friday October 27, 1:30-3:00 Fields Institute, Room 210
    Asger Tornquist, University of Toronto
    Non-classification Theorems for conjugacy and orbit equivalence of measure preserving ergodic actions, Part III.
    Abstract: We show that for a countable group G with an infinite normal subgroup H, the measure preserving ergodic a.e. free H actions that can be extended to an a.e. free measure preserving G action cannot be classified up to conjugacy (as H actions) by countable structures. This implies that for a countable group G with the relative property (T) over an infinite normal subgroup, the a.e. free ergodic G-actions cannot be classified up to orbit equivalence by countable structures.
  9. Friday October 20, 1:30-3:00 Fields Institute, Room 230
    Frank Tall, University of Toronto. Further topological applications of PFA(S)[S]
  10. Friday October 13, 1:30-3:00 Fields Institute, Room 210
    Frank Tall, University of Toronto. Locally compact spaces, paracompactness, and large cardinals.
    Abstract: By considering localized reflection principles and non-reflecting stationary sets, we distinguish the consistency strength of two propositions concerning the paracompactness of locally compact normal spaces.
  11. Friday October 6, 1:30-3:00 Fields Institute, Room 210
    Asger Tornquist University of Toronto. Non-classification theorems for conjugacy and orbit equivalence of measure preserving ergodic actions (PART II).
  12. Friday September 29, 1:30-3pm Fields Institute, Room 210
    Asger Tornquist University of Toronto. Non-classification theorems for conjugacy and orbit equivalence of measure preserving ergodic actions.
    Abstract: We give a new proof and a strengthening of a Theorem of Foreman and Weiss, stating that the measure preserving a.e. free ergodic actions of a countably infinite group cannot be classified up to conjugacy by countable structures. Using this strengthened version, we show that the measure preserving ergodic a.e. free actions of a countable group with the relative property (T) over an infinite normal subgroup cannot be classified up to orbit equivalence by countable structures.
  13. Friday, September 22, 1:30-3pm. Fields Institute
    Frank Tall, University of Toronto.PFA(S)[S] and Small Dowker Spaces.
    Abstract: There have been only a few consistency results excluding particular kindsof "small" examples of normal spaces with product with the unit interval notnormal, but a plethora of consistency results providing such examples. Werestore the balance, using a model of Todorcevic.
  14. Friday, July 21, 1:30pm-3pm. Fields Institute
    Peter Komjath, Eotvos University. Uncountable chromatics triple systems.
    Abstract: We investigate which finite systems must occur in every uncountably chromatic triple system.
  15. Friday, June 9, 1:30-3:00. Fields Institute, 210.
    Piotr Koszmider, Universidade de Sao Paulo. TBA.
  16. Friday, June 2. No seminar - Canadian Mathematical Society Summer Meeting in Calgary.
  17. Friday, May 26, 1:30-3:00. Fields Institute, 210.
    Jordi Lopez Abad, Universite Paris 7. Partial unconditionality and pre-compact families of finite sets.
  18. Friday, May 19. No seminar - ASL Annual Meeting in Montreal.
  19. Friday, May 12, 1:30-3:00. Fields Institute, 210.
    James Hirschorn, Kobe University. Characterizing the quasi ordering of the irrationalsby eventual dominance.
  20. Tuesday, May 9, 3:30-5:00. Fields Institute, 230.
    Dusan Repovs, University of Ljubljana: Geometric topology of Cantor sets. Note the unusual date and time.
    abstract.
  21. Friday, May 5. 1:30-3:00. Fields Institute, 210.
    Paul J. Szeptycki, York: Transversals of strongly almost disjoint families.
  22. Friday, April 28, 2006. 1:30-3:00. Fields Institute, 210.
    Ari Meir Brodsky, University of Toronto: A partition theorem for triples in nonspecial trees, part 2.
  23. Friday, April 21, 2006. 1:30-3:00. Fields Institute, 210.
    Joel D. Hamkins, CUNY Graduate Center and College of Staten Island: The modal logic of forcing.
    What are the most general principles relating forceability and truth? As in Solovay's celebrated analysis of provability, this question and its answer are naturally formulated in modal logic. Specifically, define that a set theoretic assertion phi is *forceable* or *possible* if it holds in some forcing extension, and *necessary* if it holds in all forcing extensions. Under this forcing interpretation, the valid principles of forcing are exactly those in the modal theory known as S4.2. This is joint work with Benedikt Loewe.
  24. Friday, April 14, 2006. Good Friday, university closed.
  25. Friday, April 7, 2006. 1:30-3:00. Fields Institute, 210.
    Ari Meir Brodsky, University of Toronto: For any nonspecial tree T and natural numbers m and n, T-->(omega+m,n)3.
  26. Friday, March 31, 2006. 3:30-5:00. Fields Institute, library.
    Barbara F. Csima, University of Waterloo: Every 1-Generic Computes a Properly 1-Generic.
    abstract.
  27. Monday, March 27, 2006. 3:30-5:00. Fields Institute, room 210. (Note the unusual day!)
    Andres E. Caicedo, Caltech: PFA and a covering property that implies SCH.
  28. Friday, March 24, 2006. 3:30-5:00. Fields Institute, library.
    Christian Rosendal, University of Illinois at Urbana-Champaign: Automatic continuity of homomorphisms in the group setting.
    I the last couple of years a number of results have surfaced to the effectthat for particular topological groups any homomorphism into a separabletopological group is continuous. This has implications for the structuretheory of the underlying discrete group and provides interesting examplesin topological dynamics. We shall consider some of these groups and theirproperties, e.g., homeomorphism groups of compact 2-manifolds.
  29. Friday, March 17, 2006. 3:30-5:00. Fields Institute, library.
    Lionel Nguyen Van The, Universite Paris 7: Divisibility properties in countable ultrahomogeneous ultrametric spaces.
    Given a countable subset S of positive reals, it is known that there is,up to isometry, a unique countable ultrametric space Q_S which is bothultrahomogeneous (any isometry between finite subspaces extends to anisometry of Q_S onto itself) and universal for the class of all countableultrametric spaces with distances in S. In this talk, we study thebehaviour of Q_S when submitted to finite and countable partitions.
  30. Friday, March 10, 2006. 3:30-5:00. Fields Institute, library.
    Stevo Todorcevic:Oscillation theory on traces, part II
  31. Friday, March 3, 2006. 3:30-5:00. Fields Institute, library.
    Stevo Todorcevic:Oscillation theory on traces, part I
  32. Friday, February 17, 2006. 3:30-5:00. Fields Institute, library.
    Ilijas Farah, York University:An exhaustive pathological submeasure, part IV (final).
  33. Friday, February 10, 2006. 3:30-5:00. Fields Institute, library.
    Ilijas Farah, York University:An exhaustive pathological submeasure, part III.
  34. Friday, February 3, 2006. 3:30-5:00. Fields Institute, library.
    Artur Tomita, Sao Paulo: Some recent examples of countably compactgroups.
    abstract
  35. Friday, January 27, 2006. 3:30-5:00. Fields Institute, library.
    Ilijas Farah, York University:An exhaustive pathological submeasure, part II.
  36. Friday, January 20, 2006. 4:00-5:30. Fields Institute, library.
    Ilijas Farah, York University:An exhaustive pathological submeasure, part I.
    Life as we have come to know it is over. I will present Michel Talagrand's solution to Maharam's problem (aka The Control Measure Problem).
  37. Friday, January 13, 2006. 4:00-5:30. Fields Institute, library.
    Frank Tall, University of Toronto.PFA(S)[S}, IV: More Topological Applications.
  38. Friday, January 6, 2006. 4:00-5:30 (note the atypical time). Fields Institute, 210.
    Slawek Solecki, University of Illinois at Urbana-Champaign, The coset equivalence relations and topologies on Borel groups.
    Let $G$ be a Polish group, and let $H$ be a Borel subgroup of$G$. By $E_{G/H}$ we denote the equivalence relation on $G$ induced by itspartition into left cosets of $H$. I will present the following result:if $H$ is Abelian, then either $E_{G/H}$ is complicated (in technicalterms: $E_1$ Borel embeds to it) or there is a necessarily unique Polishgroup topology on $H$ including the topology inherited from $G$. Thisresult is related to certain conjectures of Kechris and Louveau. I willpresent background of the theorem and give some details of its proof.
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