We are pleased to announce that the Set Theory, Logic and Topology department of the Alfréd Rényi Institute of Mathematics and the Department of Logic of Eötvös Loránd University organize a mini-wokrshop celebrating the 2nd World Logic Day at 14 January 2020.
"A dynamic and global annual celebration of World Logic Day aims at fostering international cooperation, promoting the development of logic, in both research and teaching, supporting the activities of associations, universities and other institutions involved with logic, and enhancing public understanding of logic and its implications for science, technology and innovation."
-- Proclamation of a World Logic Day UNESCO. General Conference, 40th, 2019.
Alfred Rényi Institute of Mathematics (Budapest, Reáltanoda u. 13-15.)
Big Lecture Hall (at the 1st floor)
- 15:30-15:55 Sándor Jenei: Algebraic Semantics for Logics Between Abelian Logic and a Relevance Logic
- Abstract: Residuated algebraic structures have been the subject of intense inquiry in recent years, primarily because of their strong connection to various substructural logics. Despite the extensive literature devoted to these classes of algebras, there are still very few results that effectively describe their structure. We make a contribution to this problem in the talk. For involutive, commutative residuated chains, where either the residual complement operation leaves the unit element fixed or the unit element is the cover of its residual complement, a representation theorem will be presented by means of linearly ordered abelian groups and a new construction.
- 15:55-16:20 Zalán Gyenis: Beth definability for fragments of first order logic
- Abstract: The talk centers around the weak Beth definability property of finite variable fragments of first order logic. We discuss the notion of strong and weak Beth definability properties and sketch the proof that the n-variable fragment (for n at least two) does not have either Beth properties.
- 16:20-16:45 Gábor Sági: The profinite topology of free groups and weaklygeneric tuples of automorphisms
- 16:45-17:10 Dorottya Sziráki: Open graphs and hypergraphs on definable subsets of higher Baire spaces
- Abstract: The open graph dichotomy for a given set X of reals is a generalization of the perfect set property for X which can also be viewed as the perfect set version of the Open Coloring Axiom restricted to X. In joint work with Philipp Schlicht, we extend a theorem of Qi Feng's about the open graph dichotomy for definable subsets of the real line to the higher Baire space κ^κ, where κ is an uncountable regular cardinal. More concretely, we show that the uncountable analogue of the open graph dichotomy for all subsets of the higher Baire space κ^κ which are definable from a κ-sequence of ordinals is consistent relative to the existence of an inaccessible cardinal above κ.
We also obtain generalizations of Qi Feng's and our above mentioned results to definable infinite dimensional hypergraphs. These concern an infinite dimensional version of the open graph dichotomy which was recently introduced by Raphael Carroy, Ben Miller and Daniel Soukup.
- 17:10-17:35 Lajos Soukup: On large κ-homogeneous, but not κ-transitive permutation groups
- 17:35-18:30 informal discussion + coffee
1st Logic day events in Hungary: at Eötvös Loránd University and at University of Pécs.