## Join-completions of ordered algebras

In this paper, coauthored with José Gil-Férez, Constantine Tsinakis, and Hongjun Zhou, we present a systematic study of join-extensions and join-completions of ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind-MacNeille completion to the proof of the finite embeddability property for a number of varieties of ordered algebras.

## Corso di “Algebra della Logica” alla scuola AILA 2017

This year I teach a course (12 hours) a the AILA summer school of logic. Below one can find the slides of my first three lectures and some references.

**Lecture 1**(Classical propositional logic and Boolean algebras)**Lecture 2**(Algebraic completeness of propositional calculus)**Lecture 3**(Abstract Algebraic Logic)**Lecture 4**(Dualities) lecture material:**Lecture 5 and 6**(Non classical logic) references:- Y. Venema, Algebras and Coalgebras, in: J. van Benthem, P. Blackburn and F. Wolter (editors),
*Handbook of Modal Logic*, 2006, pp 331-426. - R. L. O. Cignoli, I. M. L. D’Ottaviano e D. Mundici,
*Algebraic Foundations of Many-Valued Reasoning*, Trends in Logic, Vol. 7 Springer, 2000.

- Y. Venema, Algebras and Coalgebras, in: J. van Benthem, P. Blackburn and F. Wolter (editors),

Lecture notes by Guido Gherardi (Computability Theory).

## Workshop on “Geometry and non-classical logics”

I am happy to announce that we will host a workshop on “Geometry and non-classical logics” at the campus of the University of Salerno, from the 5th to the 8th of September.

The workshop is one of the events planned within the EU-funded project SYSMICS.

Further information can be found at http://logica.dipmat.unisa.it/sysmics/geoNonLogic/

## The Twelfth International Tbilisi Symposium on Language, Logic and Computation

The Twelfth International Tbilisi Symposium on Language, Logic and Computation will be held on **18-22 September 2017** in Kakheti, Georgia. The Programme Committee invites submissions for contributions on all aspects of language, logic and computation: https://easychair.org/conferences/?conf=tbillc2017. Submission deadline: **15 March 2017**.

#### Tutorials:

*Language*: Jakub Szymanik (University of Amsterdam)

*Logic*: Sam van Gool (City College of New York)

*Computation*: Ana Sokolova (University of Salzburg)

#### Invited speakers:

*Language*:

Gemma Boleda (Universitat Pompeu Fabra)

Ruth Kempson (King’s College, London)

*Logic*:

Alexander Kurz (University of Leicester)

Eric Pacuit (University of Maryland)

*Computation*:

Dexter Kozen (Cornell University)

Alex Simpson (University of Ljubljana)

Further information at http://events.illc.uva.nl/Tbilisi/Tbilisi2017/

## PhD Course on Category Theory (Jan-Feb 2017)

## Page contents

## News

## Contents

- Categories and functors. Universal objects.
- Natural transformations. Adjoint functors and equivalences.
- Dualities: Stone, Gelfand, Pontryagin.

## Course material

- Harold Simmons. An Introduction to Category Theory. (2011) Cambridge University Press.
- Saunders Mac Lane. Categories for the Working Mathematician (Second edition). Springer.

### Homework

- Homework set 1
- Homework 2: prove that the three definitions of adjoint functors are equivalent. Skip the easiest details.

## Practicalities

- Lecturer: Luca Spada
- Length of the course:
**10 hours**.

### Dates/rooms:

- Lectures will take place is
*Sala Riunioni,*Department of Mathematics. - Lectures will be scheduled as follows:
- Tuesday 17 of January, from 11:00 to 13:00;
- Thursday 19 of January, from 11:00 to 13:00;
- Tuesday 24 of January, from 11:00 to 13:00;
- Thursday 26 of January, from 11:00 to 13:00;
- Tuesday 7 of February, from 11:00 to 13:00;

**Comments, complaints, questions**: please write to Luca Spada