Tuesday 22
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4:10 pm, room 1308. Special Colloquium.
Tea at 3:30 pm in SC 1425.
4:10-5:30 pm, room 1432. Universal
Algebra
and Logic Seminar. Ciro Russo, Vanderbilt University. Propositional deductive systems: hidden interpretability, fragments and equivalence. The interpretability of one logic into another is a very common issue in Mathematical Logic but, as far as we know, a precise and general definition of the concept of "interpretation" is still lacking, the meaning of this word usually relying on a logician's intuition. We propose a general and purely syntactic definition of interpretability for the case of propositional deductive systems. Then we generalize this definition, together with the notions of equivalence of deductive systems and a fragment of a logic, to corresponding "hidden" notions. Such generalizations are amenable to an algebraic characterization that, under additional hypotheses, yield results for the corresponding non-hidden notions.
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