DOCTORATE DEGREE (PhD)

Students who successfully complete the research track of the Master in Pure and Applied Logic will be prepared to initiate a research career at an international level, in the area of Logic where they have specialized.

The lecturers at the Master, as well as other researchers of their groups, can supervise research work leading to the Spanish official title of Doctor in the Official Postgraduate Programs (POP) of the catalan universities. Below you can see the research areas of these lecturers and researchers.

The list of the relevant POPs is not completely determined yet, but it is expected that it will include at least the following ones:

• Computation (Technical University of Catalonia)
• Mathematics (University of Barcelona)
• Mathematics and Statistics (Technical University of Catalonia)
• Philosophy (University of Barcelona)

According to the Spanish regulations presently in force, admittance to the Doctorate (PhD) Program can be granted to all candidates that meet the official requirements (Article 10.3 of Royal Decree 56/2005). These state that candidates should hold a Spanish master degree, or have completed at least 60 credits on a master program provided that they have earned a total of at least 300 credits between their undergraduate and postgraduate studies. Additionally, candidates must be able to demonstrate that they have the necessary grounding and expertise to undertake their research project. More details may be found, in near future, in the web pages of the University of Barcelona and the Technical University of Catalonia.

Research areas

• Universal Algebra (Antoni Torrens)
• Computational Complexity (José Luis Balcázar, Albert Atserias)
• Complexity of Proofs (Maria Lluïsa Bonet)
• Automatic Theorem Proving (Maria Lluïsa Bonet)
• Philosophy of Logic and Mathematics (Ignasi Jané)
• History of Logic (Calixto Badesa)
• Computational Linguistics: Grammar as a substructural logic, applications of logic to grammar and natural language processing (Glyn Morrill)
• Algebraic Logic: Abstract algebraic logic, classification of logics in the Leibniz and Frege hierarchies, theory of algebraization of Gentzen calculi, duality between algebraic semnatics and relational semantics (Kripke style), study of the algebraization of specific logics (Josep Maria Font, Ramon Jansana, Joan Gispert, Antoni Torrens, Ventura Verdú)
• Categorical Logic: Models for elementary set theory in certain categories (generalizations of topoi), categorical semantics for lambda calculi and type theory (Raimon Elgueta)
• Non-Classical Logics: Many-valued logics (algebraic study of extensions of Lukasiewicz's infinite valued calculus and of t-norm based logics, of fragments of certain many-valued, linear and relevance logics), Modal logic (study of fragments), Substructural logics (new theoretical issues raised by the applications of substructural logics to computer science and computational linguistics), Foundations of fuzzy logic (Francesc Esteva, Josep Maria Font, Pere Garcia, Ramon Jansana, Joan Gispert, Glyn Morrill, Antoni Torrens, Ventura Verdú)
• Set Theory: Forcing, descriptive set theory, set theory of the real numbers, infinite combinatorics, generic absoluteness, forcing axioms, applications of set theory to topology and analysis, structure of Boolean algebras determined by cardinality functions and by the sequence of cardinals determined by the Cantor-Bendixson derivative (Joan Bagaria, Juan Carlos Martínez, Ignasi Jané)
• Model Theory: General model theory, model theory applied to algebra, finite model theory, stability, simple theories (Albert Atserias, Enrique Casanovas, Rafel Farré)

The Master in Pure and Applied Logic draws and builds on the expertise acquired from more than a decade of postgraduate courses offered as part of the University of Barcelona's Doctorate Program in Logic and Foundations of Mathematics. Click here to browse the list of PhD theses completed as part of this program.