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

Coalgebraic Semantics for Fischer Servi Intuitionistic Modal Logic

Authors: Rodrigo Nicolau Almeida, Nick Bezhanishvili and Sarah Dukic

Accepted at CMCS 2026 • February 2026

Pre-Printed Notes

Uniform local tabularity in intuitionistic logic

Authors: Rodrigo Nicolau Almeida

• January 2026

Structural Completeness in bi-IPC

Authors: Rodrigo Nicolau Almeida and Nick Bezhanishvili

• August 2025

Submitted Articles

Superamalgamation for modal lattices via non-distributive dualities

Authors: Rodrigo Nicolau Almeida, Nick Bezhanishvili and Simon Lemal

• Submitted on 25 Feb 2026 (v1)

Esakia order-compactifications and locally Esakia spaces

Authors: Rodrigo Nicolau Almeida, Guram Bezhanishvili and Nick Bezhanishvili

• Submitted on 26 Dec 2025 (v1)

Colimits of Heyting Algebras through Esakia Duality

Authors: Rodrigo Nicolau Almeida

• Submitted on 12 Feb 2024 (v1), last revised 13 Nov 2024 (this version, v3)