Research Statement
My current research focuses broadly on Heyting algebras and closely related structures. In them I am particularly interested in the study of technical questions on the structure of the category of Heyting algebras, such as providing descriptions of ordered compactifications of ordered topological spaces, or describing free objects in these and associated categories; and properties of classes of Heyting algebras, such as the study of lattices of varieties and quasivarieties, the distribution of properties like structural completeness, interpolation or tabularity; as well as the study non-standard rules, such as Pi-2-rules, in their universal-algebraic aspects and their computational properties.
I am broadly interested in universal algebra, model theory and category theory, and especially their interaction.
In a previous academic life I was a researcher in sociology of culture. I worked on policy analysis and briefly on agent-based modelling. You can find most of my work related to that in this link.
Published Articles
Maximality Principles in Modal Logic and the Axiom of Choice
Authors: Rodrigo Nicolau Almeida, Guram Bezhanishvili
Fundamenta Mathematicae, Volume 271, October 2025, Pages 173-193 • 2025
A Coalgebraic Semantics for Intuitionistic Modal Logic
Authors: Rodrigo Nicolau Almeida, Nick Bezhanishvili
Advances in Modal Logic, Volume 15, August 2024, Pages 59-77 • 2024
Unification with Simple Variable Restrictions and Admissibility of Pi2-rules
Authors: Rodrigo Nicolau Almeida, Silvio Ghilardi
Advances in Modal Logic, Volume 15, August 2024, Pages 79-100 • 2024
Π2-rule systems and inductive classes of Gödel algebras
Authors: Rodrigo Nicolau Almeida
Annals of Pure and Applied Logic, Volume 176, Issue 4, April 2025 • 2025
Polyatomic logics and generalized Blok–Esakia theory
Authors: Rodrigo Nicolau Almeida
Journal of Logic and Computation, Volume 34, Issue 5, July 2024, Pages 887–935 • 2023
Accepted Articles
Uniform local tabularity in intuitionistic logic
Authors: R.N. Almeida
Accepted at AIML 2026. Extended version available here. • April 2026
Coequivalence relations and descent in modal logic
Authors: R.N. Almeida and Matteo De Berardinis
Accepted at AIML 2026. • April 2026
Coalgebraic Semantics for Fischer Servi Intuitionistic Modal Logic
Authors: R.N. Almeida, Nick Bezhanishvili and Sarah Dukic
Accepted at CMCS 2026 • February 2026
Pre-Printed Notes
Colimits of Heyting Algebras through Esakia Duality
Authors: R.N. Almeida
• Submitted on 12 Feb 2024 (v1), last revised 13 Nov 2024 (this version, v3)
Submitted Articles
A topos for étale-finite Heyting algebras
Authors: Marco Abbadini, R.N. Almeida and Igor Arrieta
• Submitted on 2 Apr 2026 (v1)
Fischer-Servi logic does not have interpolation
Authors: R.N. Almeida, Nick Bezhanishvili and Simon Lemal
• Submitted on 2 Apr 2026 (v1)
Superamalgamation for modal lattices via non-distributive dualities
Authors: R.N. Almeida, Nick Bezhanishvili and Simon Lemal
• Submitted on 25 Feb 2026 (v1)
Esakia order-compactifications and locally Esakia spaces
Authors: R.N. Almeida, Guram Bezhanishvili and Nick Bezhanishvili
• Submitted on 26 Dec 2025 (v1)