6th Annual Graduate Student Conference in Logic

Smautf has calculated that in 1978 there would be two thousand one hundred eighty-seven new members of the sect of The Three Free Men, and, assuming none of the older disciples dies, a total of three thousand two hundred and seventy-seven keepers of the faith. Then things would go much faster; by 2017, the nineteenth generation would run a more than a thousand million people. In 2020, the entire planet, and well beyond, would have been converted.

G. Perec, Life: A user's manual

• Conference announcement and Call for Papers
• Program
• People we know are coming
• Contacts

Program

Conference Announcement and Call for Papers

The Graduate Student Conference in Logic is designed to give graduate students doing work in logic the opportunity to deliver and hear talks, as well as develop peer contacts in the field. It will run from Saturday April 23 to Sunday April 24, 2005. Professors are welcome to attend the talks and encouraged to send their students.

All talks will be delivered by student participants (with the exception of one keynote address). Talks will be either 20 or 45 minutes long and should be aimed at other students in the field. This conference is a good opportunity to practice giving research-oriented talks in a professional setting. We welcome talks about original research, but also about the work of others. Since the talks will be aimed at graduate students, we hope they will accessible to most attendees.

There is no registration fee, but please let us know if you plan to come by March 15. If you require housing, let us know and we will do our best to find a couch or floor space for you. Alternatively, there are several hotels nearby (check out for example http://www.cucvb.org/accom/index.html for some information).

Abstracts should be sent to one of the organizers (see Contacts), and are to be received by March 15. Please indicate the length of time you would like your talk to be (20 or 45 minutes).

People we know are coming

• Alexander Raichev
• Asher Kach
• James Hunter
• Nicolas Addington
• Daniel Mcginn
• Christopher Alfeld
• Thomas Kent
• David Milovich
• Benjamin Ellison
• Jaime Posada
• Elisa Vasquez
• Erik Andrejko
• Eugene Tsai
• Kathleen Kiernan
• Rob Owen
• Paul Pederson

• Saleh Aliyari

• Javier Moreno
• Hernando Tellez
• Dominika Polkowska
• Ayhan Gunaydin
• Jana Marikova
• Jojo Dong
• Salih Azgin
• Sylvia Carlisle
• Maciej Malicki
• Pedro Poitevin
• Konstantinos Schoretsanitis
• Sonat Suer

Abstracts

• Pedro Poitevin (UIUC)
  Basic Model Theory of Nakano spaces.

  Nakano spaces are generalizations of L_p spaces in which p is allowed to vary measurably with the underlying measure space. Equipped with a modular, Nakano spaces turn out to admit elimination of quantifiers. We will attempt to outline a proof of this result.

• Alex Raichev (UW)
  Bring your daughter... to the slaughter.

  I will present some recent results in the field of relative randomness via rK-reducibility. That's right, I'm going to talk about my thesis. No animal (or human) will be harmed.

• Saleh Aliyari (UI)
  Topological Frames and their logic.

  Modal algebras, and in general, Boolean algebras with operations (BAO's), play a role "almost" dual to that of Kripke frames. However the category of Modal algebras and Kripke frames are not dual in the sense of category theory. It is also known that Descriptive General Frames, which are based on Kripke frames, make a perfect dual to modal algebras. From a coalgebraic point of view, Kripke frames are Coalgebras of the power set functor over Sets. It was recently noted by Kupke, et al, that one can consider DGF's as coalgebras of the Vietoris functor on the Cateogry of Stone spaces, which are aompact, Hausdorff and totally disconnected spaces. . The idea is based on Stone representation theorem. This can lead us to restate certain known facts in more appealing/intuitive terms.

  Although equivalence of these topological frames (sv-frames, as I call them) with DGF's was noted by Kupke, et al, they did not analyse the logic of these frames. Through, connections with the category of Modal Algebras, I have proved certain properties for classes of sv-frames, such as Hessney-Milner property, and also I have used the dulaity, to prove certain "definability/determinacy" conditions for classes of modal algebras.

• Javier Moreno (UIUC)
  Pulling groups out of hats.

  Under certain nice assumptions you can turn automorphism groups into definable groups. Behind those tricks there is the general theory of internality and binding groups. I'll define what internality is and give you a few examples of places where you can apply these results.

• Jojo Dong (UIUC)
  Extending partial automorphisms and the profinite topology on free groups.

  I will state (without proof) Herwig and Lascar's main result in Extending partial automorphisms and the profinite topology on free groups (Transations of the American Mathematical Society 352 (1999)). Then I will indicate relations between this result, a theorem on extending partial automorphisms of finite graphs due to Hrushovski, and two theorems about the profinite topology on free groups, one due to Hall and the other due to Ribes and Zalesskii.

• Chris Alfeld (UW)
  Non-Branching Degrees in the Medvedev Lattice of Pi01 classes.

  A $\Pi^0_1$ class is the set of infinite paths through a computable tree. We say that $P \geq_m Q$ if there is a computable function $f$ which maps $P$ into $Q$. The Medvedev lattice of $\Pi^0_1$ classes is the lattice of degrees induced by this reduction. I will provide background and give characterizations and results about non-branching degrees in this lattice. In particular I will show three distinct classes of non-branching degrees.

• James Hunter (UW)
  The Baire Category Theorem in Reverse Mathematics.

  One standard formulation of the Baire Category Theorem —"The intersection of a countable number of dense open sets is dense"—is provable in RCA_0; the proof follows directly from the definition of a real number in RCA_0.

  However, a perhaps more useful formulation of the Baire Category Theorem based on "separably closed" (vs. "closed") sets is not provable in RCA_0 nor in the stronger system WKL_0. These two definitions for closed sets are not equivalent under the more restrictive subsystems of second-order arithmetic; "separably closed" and "closed" sets being equivalent requires the even stronger system ACA_0.

  I present a brief overview of papers by Douglas Brown and Stephen Simpson, and Michael Mytilinaios and Ted Slaman, on two formulations of the Baire Category Theorem.

• Ayhan Gunaydin (UIUC)
  The fields of complex and real numbers with a "small" multiplicative group.

  We axiomatize the theory of structures (K,G), where K is an algebraically closed of real closed field and G is a "small" multiplicative subgroup of K^x. We also give a description of definable sets in (K,G). In order to capture the notion of "smallness", we introduce the "Mann property" for a multiplicative group of a field.

• Jana Marikova (UIUC)
  Type-definable groups in o-minimal structures

  Let M be a big o-minimal structure and G a type-definable group in Mⁿ. Then G is a type-definable subset of a definable manifold in Mⁿ that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomrphic to a type-definable group in some M^k with the topology induced by M^k. Part of this result holds the wider class of so-called \iota-groups.

  This is work based on reading classes with Y. Peterzil and L. van den Dries.

Contacts

• Hernando Tellez htellez(at)math.uiuc.edu
• Javier A. Moreno jamoreno(at)math.uiuc.edu