Toronto Set Theory Seminar - Year 2005.

1. Friday, December 2, 2005. 1:30-3:00. Fields Institute, room TBA.
   Frank Tall, University of Toronto. Mutually consistent topological consequences of PFA and V = L, II.
   
2. Friday, November 25, 2005. 1:30-3:00. Fields Institute, room TBA.
   Frank Tall, University of Toronto. Mutually consistent topological consequences of PFA and V = L, I.
   Models of form PFA(S)[S] have recently been used to solve several difficult topological problems. In these models, a variety of useful consequences of the mutually contradictory axioms PFA and V = L hold. In this first talk, we will give a simple PFA proof of the existence of certain disjoint compact G-delta expansions of closed discrete subspaces of locally compact normal spaces. In later talks, we will show how to modify the proof to work in a PFA(S)[S] context, wherein the Souslin forcing will enable us to make the expansions open. This project leads to results such as the consistency of locally compact hereditarily normal spaces being paracompact if and only if they do not include a perfect preimage of omega_1. Familiarity with the proof that PFA implies there are no S-spaces will be assumed.
   
3. Friday, November 18, 2005. 3:30-5:00. Fields Institute, room TBA.
   Efren Ruiz, University of Toronto. C*-algebras and their representations, part II
   
4. Friday, November 11, 2005. 3:30-5:00. Fields Institute, room TBA.
   Efren Ruiz, University of Toronto. C*-algebras and their representations
   
5. Friday, November 4, 2005. 1:30-3:00. Fields Institute, room 210.
   Michael Ray Oliver, York. Borel cardinality of collection of quotient Boolean algebras: The Director's Cut, part II
   
6. Friday, October 28, 2005. 1:30-3:00. Fields Institute, room 210.
   Michael Ray Oliver, York. Borel cardinality of collection of quotient Boolean algebras: The Director's Cut
   
7. Friday, October 21, 2005. 1:30-3:00. Fields Insitute, room 210.
   Stuart Zoble, University of Toronto: Bounding for L and L(R)
   
8. Friday, October 14, 2005. 1:30-3:00. Fields Institute, room 210.
   Ilijas Farah, York University: Nonstationary ideal and the Continuum Hypothesis III
   
9. Friday, October 7, 2005. 1:30-3:00. Fields Institute, room 210.
   Ilijas Farah, York University: Nonstationary ideal and the Continuum Hypothesis II
   
10. Friday, October 4, 2005, 2:30-3:30. McMaster University, Hamilton Hall, room 312, at McMaster Logic Colloquium,
    Ilijas Farah will speak about Maharam's Problem.
11. Friday, September 30, 2005. 1:30-3:00. Fields Institute, room 210.
    Ilijas Farah, York University: Nonstationary ideal and the Continuum Hypothesis.
    I will present Woodin's proof that the saturatedness of the nonstationary ideal on omega_1 and the existence of a measurable cardinal imply CH fails. I will include all the necessary background material, so that everyone familiar with forcing will be able to follow.
    
12. Special Event: Departmental Colloquium at York.
    Thursday, September 29, 3:30pm. N638 Ross.
    David H. Fremlin, University of Essex and York. Set-theoretic Measure Theory.
    As soon as Paul Cohen showed in 1964 that the continuum hypothesis is not provable in ZFC, it was evident that many questions in abstract analysis were likely to be undecidable. In this talk I will discuss some of the topics in measure theory, both on the real line and in abstract measure spaces, in which such questions have led to substantial new theorems of ZFC, and in turn to new problems.
    Refreshments will be served in N620 Ross prior to the talk.
13. Friday, September 23, 2005. 1:30-3:00. Fields Institute, room 210.
    David H. Fremlin, University of Essex and York. Topological spaces after forcing II.
    
14. Friday, September 16, 2005. 1:30-3:00. Fields Institute, room 210.
    David H. Fremlin, University of Essex and York. Topological spaces after forcing
    An attempt to devise a general structure for discussion of what can be expected of a construction for a Hausdorff space if performed in a forcing model.
    
15. Friday, September 9, 2005. 1:30-3:00. Fields Institute, room 210.
    Michael Ray Oliver, York. Borel cardinality of the collection of quotient Boolean algebras
    
16. Friday, September 2, 2005. 1:30-3:00. Fields Institute, room 210.
    James Hirschorn, Kobe University. A general preservation theorem for proper countable support iterations III
    
17. Friday, August 26, 2005. 1:30-3:00. Fields Institute, room 210.
    James Hirschorn, Kobe University. A general preservation theorem for proper countable support iterations II
    
18. Friday, August 19, 2005. 1:30-3:00. Fields Institute, room 210.
    James Hirschorn, Kobe University. A general preservation theorem for proper countable support iterations
    
19. Friday, August 5, 2005. 1:30-3:00. Fields Institute, room 210.
    Fernando Hernandez Hernandez, Instituto de Matematicas UNAM, Morelia: sup vs max on $\lambda$-sets.
    
20. Friday, July 29, 2005. 1:30-3:00. Fields Institute, room 210.
    Ilijas Farah, York University: Uniformly exhaustive submeasures are not pathological, part II.
    I will complete the proof of the 1984 theorem of Kalton and Roberts from the title.
    
21. Friday, July 22, 2005. 1:30-3:00. Fields Institute, room 210.
    Ilijas Farah, York University: Uniformly exhaustive submeasures are not pathological.
    I will give a proof of the 1984 theorem of Kalton and Roberts from the title.
    
22. Friday, July 15, 2005. 1:30-3:00. Fields Institute, room 210.
    Juris Steprans, York University: A regular CLP-compact space of countable tightness whose square is not CLP-compact, part II.
23. There will be no seminar on Friday, July 1.
24. Friday, June 24, 2005. 1:30-3:00. Fields Institute, room 210.
    Maxim R. Burke, UPEI: Liftings for category algebras
    For a Baire topological space X, the algebra of sets having the property of Baire modulo the ideal of first category sets is analogous, from some points of view, to the measure algebra of a measure space. In particular, the theory of liftings for such algebras has many points in common with the theory of liftings for measure spaces, including many of the same open problems. We discuss some of the results and some of the open problems of this theory.
25. Friday, June 17, 2005. 1:30-3:00. Fields Institute, room 210.
    Juris Steprans, York University: A regular CLP-compact space of countable tightness whose square is not CLP-compact.
26. Friday, June 10, 2005. 1:30-3:00. Fields Institute, room 210.
    Ilijas Farah, York University: Prikry problem for Suslin forcings.
    A forcing P is Suslin if P is an analytic set of reals and both of its compatibility and the incompatbility relations are analytic. It is an open problem whether every Suslin ccc forcing adds a Cohen or a random real. I will show that for every Suslin ccc forcing P the product PxP adds a Cohen real. This is a joint work with Boban Velickovic.
27. Friday, May 13, 2005. 1:30-3:00. Fields Institute, room 210.
    Dikran Dikranjan, York University and University of Udine Characterizing subgroups of the circle and of the compact abelian groups.
    The interest in the distribution, modulo 1, of the mutliples m_n.a of an irrational number a, where m=(m_n) is a given sequence of integers, has deep roots in number theory (Weyl's theorem of uniform distribution modulo 1), analysis (convergence of trigonometric series) and ergodic theory (Sturmian sequences and Hartman sets), beyond topology and descriptive set theory. It is more natural and also more convenient to consider this issue on the (compact) circle g roup T=R/Z. The subgroup t_m(T) of all elements x of T such that m_n.x converges to 0 has been extensively studied by many authors (Braconnier and Vilenkin in the forties etc.) and in more general situation (replacing T by a locally compact group). Recently, Biro', Deshouillers and So's, answering questions of A. Stone and D. Maharam, proved that every countable subgroup of T can be characterized as t_m(T) for an appropriate sequence m. Their proof contains a gap. The talk will discuss recent joint work in this direction with K. Kunen, C. Milan, R. Di Santo and A. Tonolo.
28. Friday, April 15, 2005. 1:30-3:00. Fields Institute, room 210.
    Juris Steprans, York University: A pigeon hole type of principle for measure spaces.
    It is easy to establish that, given a measurable mapping from the product of measure spaces to another measure space there is a subset of the range of arbitrarily small measure whose pre-image contains either a vertical section or function or arbitrarily large measure. Generalizing this to higher dimensions seems to require large cardinals.
    
29. Friday, April 15, 2005. 1:30-3:00. Fields Institute, room 210.
    Goyo Mijares, Universidad Central de Venezuela: Parametrizing the abstract Ellentuck theorem, part III.
    
30. Friday, April 8, 2005. 1:30-3:00. Fields Institute, room 210.
    Goyo Mijares, Universidad Central de Venezuela: Parametrizing the abstract Ellentuck theorem, part II.
    
31. Friday, April 1, 2005. 1:30-3:00. Fields Institute, room 210.
    Goyo Mijares, Universidad Central de Venezuela: Parametrizing the abstract Ellentuck theorem.
    
32. Friday, March 25, 2005 - Good Friday, no seminar.
    
33. Friday, March 18, 2005. 1:30-3:00. Fields Institute, room 210.
    Lionel Nguyen Van The, Universite Paris 7: Partitioning Ultrametric Urysohn spaces, part II.
    
34. Friday, March 11, 2005. 1:30-3:00. Fields Institute, room 210.
    Lionel Nguyen Van The, Universite Paris 7: Partitioning Ultrametric Urysohn spaces.
    In the late 20s, P. Urysohn constructed a complete metric space U in which any separable metric space embeds isometrically and where any finite isometry between finite subspaces extends to an isometry from U onto itself. Urysohn space is now known to have several analogues and the goal of this talk is to present how these objects look like in the ultrametric setting and how they behave when partitioned into finitely many pieces.
    
35. Friday, March 4, 2005. Mini-conference in set theory.
36. Monday, February 28, 2005, 1:30-3:30. Fields Institute, room 210.
    Paul B. Larson, Miami University: Pmax and the nonstationary ideal..
37. Friday, February 25, 2005, 1:30-3:30. Fields Institute, room 210.
    Stuart Zoble, University of Toronto: Proving Projective Determinacy
38. Friday, February 18, 2005 - no seminar (reading week).
39. Friday, February 11, 2005, 1:30-3:30. Fields Institute, room 210.
    Ilijas Farah, York University: Von Neumann's problem and large cardinals
    I will show that a positive answer to von Neumann's 1937 problem on characterization of measure algebras, if consistent at all, implies the existence of inner models with measurable cardinals. More precisely, if every ccc weakly distributive complete Boolean algebra is a Maharam algebra then there is an inner model with a measurable cardinal kappa of Mitchell order at least kappa++. The proof uses some ideas of Gitik and Shelah. This complements recent results of Balcar-Jech-Pazak and Velickovic, who proved that the P-ideal dichotomy implies every ccc weakly distributive Boolean algebra is a Maharam algebra. This result reduced Von Neumann's problem to the problem whether every Maharam algebra is a measure algebra, also known as Maharam's Problem or Control Measure Problem. This is a joint work with Boban Velickovic.
40. Friday, February 4, 2005, 1:30-3:00. Fields Institute, room 210.
    Stevo Todorcevic Biorthogonal systems and quotient spaces via Baire category methods, part IV
41. Friday, January 28, 2005, 1:30-3:00. Fields Institute, room 210.
    Stevo Todorcevic Biorthogonal systems and quotient spaces via Baire category methods, part III
42. Friday, January 21, 2005, 1:30-3:00. Fields Institute, room 210.
    Stevo Todorcevic Biorthogonal systems and quotient spaces via Baire category methods, part II
43. Friday, January 14, 2005, 1:30-3:00. Fields Institute, room 210.
    Stevo Todorcevic Biorthogonal systems and quotient spaces via Baire category methods.
44. Friday, January 7, 2004, 1:30-3:00. Fields Institute, room 210.
    Slawek Solecki, University of Illinois, Urbana-Champaign: Local amenability and measure small sets.
    I will talk about a class of Polish groups which is closely related to a notion of measure small sets (left Haar null sets). The definition of this class of groups is obtained by suitably localizing to the identity element of the notion of amenability. I will present results on the extent of this class. For such groups left Haar null sets have many desired properties (they are a $\sigma$-ideal and have the Steinhaus property). I will give proofs of these results. It turns out that opposite to Polish groups which are amenable at the identity are Polish groups which have a non-Abelian free subgroup at the identity. I will make this precise. For such groups left Haar null sets lose the essential properties they enjoy for amenable at $1$ groups. I will present these results as well.