Forthcoming events in this series
16:00
Research Workshop 2 on 'Duality Theory in Algebra, Logic and Computer Science'.
Abstract
Organisers: Hilary Priestley, Drew Moshier and Leo Cabrer.
This will be devoted to the applications of dualities to logic and algebra, focusing on general techniques. Thus it will seek to complement the specialised coverage in meetings devoted to, for example, modal logic, residuated structures and many-valued logics, or coalgebras. The featured topics for the Workshop will be drawn from completions of ordered structures, and applications; admissible rules, unification theory, interpolation and amalgamation; aspects of many-valued and substructural logics and ordered algebraic structures. Keynote speakers will be Leo Cabrer and Mai Gehrke.
'Galway' Topology Symposium.
Abstract
Chief Organiser: Shari Levine. Main speakers: Alexander Arhangel'skii, Alan Dow, Aisling McCluskey, Jan van Mill, Frank Tall, Vladimir Tkachuk
Contact for further information: @email
A space that admits all possible orbit spectra of homeomorphisms of uncountable compact metric spaces
Abstract
Joint work with: Sina Greenwood, Brian Raines and Casey Sherman
Abstract: We say a space $X$ with property $\C P$ is \emph{universal} for orbit spectra of homeomorphisms with property $\C P$ provided that if $Y$ is any space with property $\C P$ and the same cardinality as $X$ and $h:Y\to Y$ is any (auto)homeomorphism then there is a homeomorphism$g:X\to X$ such that the orbit equivalence classes for $h$ and $g$ are isomorphic. We construct a compact metric space $X$ that is universal for homeomorphisms of compact metric spaces of cardinality the continuum. There is no universal space for countable compact metric spaces. In the presence of some set theoretic assumptions we also give a separable metric space of size continuum that is universal for homeomorphisms on separable metric spaces.
Non-separable Effros Theorem, and shift compactness versus ample genericity
16:00
Duality and Sahlqvist theorem fro Vietoris coalgebras on compact Hausdorff spaces.
When you can put a linear order on a set so that an arbitrary self map on that set is order preserving?
16:00
Topological dualities for distributive meet-semilattices, implicative semilattices and Hilbert algebras
Abstract
I will first present Priestley style topological dualities for
several categories of distributive meet-semilattices
and implicative semilattices developed by G. Bezhanishvili and myself.
Using these dualities I will introduce a topological duality for Hilbert
algebras,
the algebras that correspond to the implicative reduct of intuitionistic logic.
14:00
Relational semantics for Belnap's "useful four-valued logic", and beyond: what Belnap should have said, but didn't
09:00
09:00
Admissibility and Unification through Natural Duality >
Abstract
Dualities of various types have been used by different authors to
describe free and projective objects in a large
number of classes of algebras. Particularly, natural dualities provide a
general tool to describe free objects. In
this talk we present two interesting applications of this fact.
We first provide a combinatorial classification of unification problems
by their unification type for the
varieties of Bounded Distributive Lattices, Kleene algebras, De Morgan
algebras. Finally we provide axiomatizations forsingle
and multiple conclusion admissible rules for the varieties of Kleene
algebras, De Morgan algebras, Stone algebras.
Interlaced Lattices
Abstract
I will give an overview of some of the most interesting algebraic-lattice theoretical results on bilattices. I will focus in particular on the product construction that is used to represent a subclass of bilattices, the so-called 'interlaced bilattices', mentioning some alternative strategies to prove such a result. If time allows, I will discuss other algebras of logic related to bilattices (e.g., Nelson lattices) and their product representation.