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.

ArXiv preprint

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:
    1. Pat Morandi’s notes on dualities,
    2. Tutorial in Buenos Aires.
  • Lecture 5 and 6 (Non classical logic) references:
    1. Y. Venema, Algebras and Coalgebras, in: J. van Benthem, P. Blackburn and F. Wolter (editors), Handbook of Modal Logic, 2006, pp 331-426.
    2. 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.


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

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: Submission deadline: 15 March 2017.


Language: Jakub Szymanik (University of Amsterdam)
Logic: Sam van Gool (City College of New York)
Computation: Ana Sokolova (University of Salzburg)

Invited speakers:

Gemma Boleda (Universitat Pompeu Fabra)
Ruth Kempson (King’s College, London)
Alexander Kurz (University of Leicester)
Eric Pacuit (University of Maryland)
Dexter Kozen (Cornell University)
Alex Simpson (University of Ljubljana)

Further information at

PhD Course on Category Theory (Jan-Feb 2017)

Page contents



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

Course material


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


  • Lecturer: Luca Spada
  • Length of the course: 10 hours.


  • 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

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