Logic group at the University of Salerno

Seminar by Dr. Emma Theart

Dr. Emma Theart (Stellenbosch University) will give a seminar on Tuesday 8 July 2025 at 10:30 in the Sala Riunioni of the Department of Mathematics. Title: Extensive morphisms Abstract: Extensivity of a category can be described as a property of coproducts in the category, namely, that they are disjoint and universal. An alternative perspective is that it is a property of morphisms in a category. This talk explores this viewpoint by introducing natural notions of Read more

By Luca Spada, ago

Seminar by Dr. Cipriano Junior Cioffo

Dr. Cipriano Junior Cioffo (University of Pisa) will give a seminar on Tuesday 3 June 2025 at 11:00 in room P18, DipMat. Title: A taxonomy of categories for relations. Abstract: In this talk, we present a taxonomy of categorical structures that abstract the category of relations. The study is conducted through a gs-monoidal lens, where “gs” refers to the garbage-share structure introduced by Corradini and Gadducci in 1999. Such structures generalize cartesian categories by relaxing their algebraic Read more

By Andrea Cappelletti, ago

Course on “Axiomatic Cohesion” by Prof. Matías Menni

Matías Menni (Univeristy of La Plata) will teach a short course in Salerno on Axiomatic Cohesion. Further details are given below. An introduction to Axiomatic Cohesion. Brief description of the course  The seminal paper reprinted in [L5] proposes to axiomatize the “distinctive internal connectedness of a topos that models all spaces of a ‘general’ combinatorial, algebraic, or smooth kind”. In the Author Commentary of [L5], Lawvere observes that “The simple idea at the core of this paper has Read more

By Luca Spada, ago

Seminar by Prof. Tommaso Moraschini

Prof. Tommaso Moraschini (University of Barcelona) will give a seminar on Thursday 15 May 2025 at 11:30 in Sala Riunioni, DipMat. Title: Implicit operations in algebra and logic. Abstract: It is well known that the partial operation of taking inverses in monoids is preserved under homomorphisms and, moreover, is definable by a first-order formula in the language of monoids. Operations of this kind—definable and preserved by homomorphisms—will be called implicit operations. Since implicit operations may go beyond the language Read more

By Andrea Cappelletti, ago

Seminar by Prof. Giuseppina Terzo

Prof. Giuseppina Terzo (Università degli Studi di Napoli) will give a seminar on Wednesday 14 May 2025 at 11:30 in Sala Riunioni, DipMat. Title: Fields with(out) generic derivations. Abstract: We explore the existence of generic derivations in field expansions. We provide examples of field expansions that admit a generic derivation. Additionally, we show that exponential fields without further compatibility conditions between derivation and exponentiation cannot support a generic derivation.(In collaboration with Antongiulio Fornasiero)

By Andrea Cappelletti, ago

Seminar by Dr. Sara Ugolini

Dott. Sara Ugolini (Artificial Intelligence Research Institute, Spanish National Research Council (IIIA-CSIC)) will give a seminar on Wednesday 7 May 2025 at 11:30 in Sala Riunioni, DipMat. Title: Almost natural semirings with difference. Abstract: In this talk, we begin by considering the semiring of the natural numbers with (truncated) difference, N = (N, +, x, -, 0, 1). Its equational theory is not recursively axiomatizable, due to the fact that one can essentially encode in it the undecidability of Hilbert’s Read more

By Andrea Cappelletti, ago

Seminar by Dr. Luca Reggio

Dott. Luca Reggio (Università degli Studi di Milano) will give a seminar on Wednesday 30 April 2025 at 11:30 in Sala Riunioni, DipMat. Title: (Ordered) compact Hausdorff spaces, axiomatically. Abstract: I will provide an overview of various approaches and results concerning the problem of axiomatising theories that arise in everyday mathematics. A prototypical example is Lawvere’s Elementary Theory of the Category of Sets, which can be understood as a “structural set theory”. I will then discuss the theory Read more

By Andrea Cappelletti, ago

Seminar by Dr. Marco Abbadini

Dott. Marco Abbadini (University of Birmingham) will give a seminar on Thursday 24 April 2025 at 10:00 in Sala Riunioni, DipMat. Title: An algebraic version of Herbrand’s theorem. Abstract: Herbrand’s theorem is a fundamental result of mathematical logic, which allows a reduction of first-order logic to propositional logic.In its simplest form, it asserts that an existential statement “exists x P(x)” with P(x) quantifier-free is provable if and only if there are finitely many terms c_1,…, c_n such that Read more

By Andrea Cappelletti, ago

Seminar by Dr. Luca Carai

Dott. Luca Carai (Università degli Studi di Milano) will give a seminar on Wednesday 23 April 2025 at 11:30 in Sala Riunioni, DipMat. Title: Free algebras and coproducts in varieties of Gödel algebras. Abstract: Free algebras in varieties of Heyting algebras play an important role in the study of superintuitionistic logics as they are, up to isomorphism, Lindenbaum-Tarski algebras. Gödel algebras, which are the Heyting algebras satisfying the prelinearity axiom (x→y)∨(y→x)=1, provide the algebraic semantics for the propositional Read more

By Andrea Cappelletti, ago