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
- first hour tutorial;
- second hour scientific talk.
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.
- 13/08/2008, Week 1
16.00 hrs: Organizational meeting.
- 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.
- 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.
- 03/09/2008, Week 4
No talk, ALC 2008 in Kobe.
- 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.
- 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.
- 01/10/2008, Week 7
No talk, Hari Raya Puasa.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.