Talks during the fall term 2017
Wed 9.8.2017 12-14, C124
Jonathan Kirby: Towards quasiminimality for complex exponentiation
Abstract: Zilber conjectured in the 1990s that the complex field equipped with the exponential function is quasiminimal: every definable subset is countable or co-countable. Recent work with Martin Bays reduces this conjecture to the conjecture that certain finite systems of equations have complex solutions. In particular, Schanuel's conjecture of transcendental number theory is no longer an obstacle. We also prove unconditionally that the complex field equipped with an approximate exponential map is quasiminimal.
Wed 6.9.2017 12-14, C124
Vadim Kulikov: The title is left as a surprise
Wed 13.9.2017 12-14, C124
Juha Kontinen: Polyteam semantics
Wed 20.9.2017 12-14, C124
Hazel Brickhill: Hyperfine Structure HFSslides.pdf
Abstract: An easy route to the fine-structural properties Godel's constructible universe, L, is normally constructed by iterating the definable power-set operation. Hyperfine structure looks more closely at where and how each constructible set is defined. I will present the basic theory of hyperfine structure, which is intuitive and easy to grasp. This can be used to prove results about L that normally require the notoriously difficult fine structure theory of Jensen, such as the existence of square sequences and morasses.
Wed 27.9.2017 12-14, C124
Hazel Brickhill: Generalised closed unbounded and stationary sets
Abstract: The notions of closed unbounded and stationary set are central to Set Theory. I will introduce a new generalisation of these notions, and describe some of their basic theory. Surprisingly for a new concept is set theory, generalised closed unbounded and stationary sets are very simple to deﬁne and accessible. They are closely related to the phenomena of stationary reﬂection and indescribability and can be characterised in terms of derived topologies. These notions are being used to answer questions about provability logic, and promise a range of further applications.
Wed 4.10.2017 12-14, C124
Tapani Hyttinen: Categoricity and universal classes
Wed 11.10.2017 12-14, C124
Fausto Barbero (University of Helsinki): Some observations about generalized quantifiers in logics of imperfect information
Wed 18.10.2017 12-14, C124
Miguel Moreno: \Sigma_1^1-complete quasiorders on weakly compact cardinals
Wed 25.10.2017 12-14, C124
Wed 1.11.2017 12-14, C124
Aleksi Saarela (University of Turku): Studying Word Equations by Geometric and Algebraic Methods
Wed 8.11.2017 12-14, C124
Wed 15.11.2017 12-14, C124
Jouko Väänänen: Internal Categoricity
Wed 22.11.2017 12-14, C124
Gil Sagi (Haifa): Logic and Natural Language
Abstract: Most of the contemporary research in logic is carried out with respect to formal, mathematical, languages. Logic, however, is said to be concerned with correct reasoning, and it is natural language that we usually reason in. Can logic keep its promise in the realm where its motivation originates? On the one hand, we have formal semanticists who study the logic of natural language, assuming it exists. On the other hand, some philosophers have denied that there is a logical consequence relation in natural language. Do they mean the same thing by ``logic’’?
The aim of this talk is twofold. First, I shall try to make sense of the question of logic in natural language in an interesting way. To this end I will refer to the works of Frege, Tarski, Carnap, Quine, Davidson, Montague, Glanzberg, among others. Second, I will propose an answer. An attempted positive response will resolve the normative aspects of logic and the descriptive aspects of natural language using a model from Frege on the normativity of logic. However, my ultimate answer to the question as explicated will be negative. Finally, I will gesture at a positive outlook based on Carnapian voluntarism.
Wed 29.11.2017 12-14, C124
Ulla Karhumäki (Manchester): Simple Groups of Finite Morley Rank with a Finitary Automorphism Group
Abstract: The Cherlin Zilber Conjecture "Simple infinite groups of finite Morley rank are algebraic groups over algebraically closed fields" is considered to be one of the main open problems in the theory of omega-stable groups of finite Morley rank. Ehud Hrushovski suggested that it can be approached by proving first that a generic automorphism of a group of finite Morley rank closely resembles the behaviour of generalized Frobenius automorphisms of algebraic groups. In my talk I try to identify some conditions on a group of automorphism of a group of finite Morley rank that make it to resemble the group Frobenius maps and allow us to prove the Cherlin-Zilber Conjecture in these specific cases. To do so, I introduce finitary automophism groups and prove that a simple group of finite Morley rank with a group of finitary automorphisms is a Chevalley group over an algebraically closed field of positive characteristic.
Wed 6.12.2017 12-14, C124
Wed 13.12.2017 12-14, C124
Miika Hannula (University of Auckland): On the complexity of inclusion logic
Wed 20.12.2017 12-14, C124