Logic Seminar in Semester I AY 2008/2009

Talks are Wednesday afternoon in Math Studio (S14#03-01)
The general scheme of the seminar is Currently it is planned to start the tutorial at 15:00 hrs and the talk at 16:00 hrs. On days where there is a Colloquium Talk, both the tutorial and the seminar talk might start later. The schedule is as follows.
  1. 13/08/2008, Week 1
    16.00 hrs: Organizational meeting.

  2. 20/08/2008, Week 2
    15.00 hrs: Johanna Franklin. Tutorial Reverse mathematics.
    16.00 hrs: Yang Yue. Talk High Minimal pairs in enumeration degrees.
    Abstract of talk: I will talk about a recent joint work with Guohua Wu and Andrea Sorbi. We showed the existence of high minimal pairs in e-degrees. Motivations and some technical point will be explained in my talk.

  3. 27/08/2008, Week 3
    15.00 hrs: Johanna Franklin. Tutorial Reverse mathematics.
    16.00 hrs: Wang Wei. Talk Uncountable embeddings into the Turing degrees.
    Abstract of talk: I will present a proof that under MA each locally countable upper semi-lattice of size the continuum can be embedded into Turing degrees. Relating history and difficulties in solving similar questions will also be addressed.

  4. 03/09/2008, Week 4
    No talk, ALC 2008 in Kobe.

  5. 10/09/2008, Week 5
    15.00 hrs: Johanna Franklin. Tutorial Reverse mathematics.
    16.00 hrs: Tan Wai Yean. Talk Modified Moore machines.
    Abstract of talk: In my talk, I will introduce modified Moore machines. This is a generalization of the Moore machine, a traditional output machine. Its advantages over the Moore machine are demonstrated. However, while the original one has a decidable first order theory, this generalization has an undecidable first order theory.

  6. 17/09/2008, Week 6
    15.00 hrs: Johanna Franklin. Tutorial Reverse mathematics.
    16.00 hrs: Wu Liuzhen. Talk The abstract condensation property.
    Abstract of talk: The abstract condensation property captures part of the content of the condensation lemmas for L, K and other "L-like" models. In this talk, I will give some consequence of this property including the diamond principle. The main results were due to Hugh W Woodin and David R Law.

  7. 01/10/2008, Week 7
    No talk, Hari Raya Puasa.

  8. 08/10/2008, Week 8
    15.00 hrs: Wu Guohua. Tutorial Intermediate degrees.
    16.00 hrs: Liu Jiang. Talk Minimal pair strategy in tt-degrees - and its application.
    Abstract of talk: We can construct minimal pair in tt-degrees using a method different from Lachlan's minimal pair method in Turing degrees. This method was introduce by Jockusch and Mohrherr. It is a powerful method in tt-degrees' construction. In this talk, we will see several application of this method in recent results.

  9. 15/10/2008, Week 9
    15.00 hrs: Wu Guohua. Tutorial Intermediate degrees.
    16.00 hrs: Li Yanfang. Talk Analytic equivalence relations induced by group actions.
    Abstract of talk: A Borel equivalence relation E on Polish spaces has "Glimm-Effros" type dichotomy, i.e., either E can be concretely classifiable or E_0 can be continuously embeded into E. But in context of analytic equivalence relations, we can only have Ulm-type classification or E_0 continuously embeded into E. In this talk, I will focus on analytic equivalence relation induced by group actions and applications of this Ulm-type dichotomy.
    17.00 hrs: Quek Yin Kang. Talk Goedel's ontological proof.

  10. 22/10/2008, Week 10
    15.00 hrs: Pavel Semukhin. Tutorial Automatic structures.
    16.00 hrs: Shen Demin. Talk The story of 0#.
    Abstract of talk: In studies of large cardinals and the constructible universe, the existence of a remarkably meaningful subset of the natural numbers, 0#, comes to our eyes. This talk will include various consequences related to issue of 0# and follow the story of the discovery of 0# to give a detailed explaination of this set.

  11. 29/10/2008, Week 11
    15.00 hrs: Pavel Semukhin. Tutorial Automatic structures.
    16.00 hrs: Yang Sen. Talk Real numbers in a subuniverse.
    Abstract of talk: Let W be an inner model of the universe. We then consider the set which consists of the real numbers in W. This set is a subset of all reals. It has many interesting properties on measure, category, perfect set property and complexity.

  12. 05/11/2008, Week 12
    15.00 hrs: Pavel Semukhin. Tutorial Automatic structures.
    16.00 hrs: Frank Stephan. Numberings optimal for learning.
    Abstract of talk: This talk extends previous studies on learnability in non-acceptable numberings by considering the question: for which criteria which numberings are optimal, that is, for which numberings it holds that one can learn every learnable class using the given numbering as hypothesis space. Furthermore an effective version of optimality is studied as well. It is shown that the effectively optimal numberings for finite learning are just the acceptable numberings. In contrast to this, there are non-acceptable numberings which are optimal for finite learning and effectively optimal for explanatory, vacillatory and behaviourally correct learning. The numberings effectively optimal for explanatory learning are the K-acceptable numberings. A similar characterization is obtained for the numberings which are effectively optimal for vacillatory learning. Furthermore, it is studied which numberings are optimal for one and not for another criterion: among the criteria of finite, explanatory, vacillatory and behaviourally correct learning all separations can be obtained; however every numbering which is optimal for explanatory learning is also optimal for consistent learning.

  13. 12/11/2008, Week 13
    15.00 hrs: Pavel Semukhin. Tutorial Automatic structures.
    16.00 hrs: Johanna Franklin. Talk Van Lambalgen's Theorem and weaker randomness notions.
    Abstract of talk: Van Lambalgen's Theorem states that each half of a Martin-Loef random real is Martin-Loef random relative to the other half. It had been previously shown that this theorem fails for weaker randomness notions like recursive and Schnorr randomness in restricted sets of Turing degrees. We show here that it fails for these randomness notions in a wider set of Turing degrees and present some results on reals that are halves of reals for which van Lambalgen's Theorem fails.
    This is joint work with Frank Stephan.
Talks from the last semester.