Grz.2 is Complete for Finite Boolean Algebras.

I present Grz.2 is complete for Finite Boolean Algebras, a draft of my upcoming paper on the subject of modal logic and Kripke semantics. In this work, I provide an accessible exposition of the Grzegorczyk axiom and give a new characterization of the modal logic Grz.2.I provide a new interpretation of the Grzegorczyk axiom and […]

Precisely how to determine the modal validities of groups

Allow me to present a preview to my upcoming research article Modal group theory, a portion of which relates to a recent publication titled The modal logic of abelian groups, authored by Sören Berger, Alexander Christensen Block, and Benedikt Löwe. Namely, the authors posed the following question. What are the propositional modal validities of group […]

The modal theory of the category of sets, June 2023

This will be a talk for the Logic Advanced Class at the Andrew Wiles Building in Oxford on the June 5th 2023 at 11 am local time. This presentation will draw upon a circulating preprint of my forthcoming article bearing the same title. The project has been supervised by Joel David Hamkins. I shall explore […]

Modal logic: a unified approach to category theory and model theory

I shall give the third in a series of talks on the unification of different parts of mathematics at the University of Gdańsk. The talk shall take place on 13 December 2022 at 10:15 local time in room 130, Faculty of Mathematics, Physics, and Informatics. Abstract. One of the central incentives of the rise of […]

Modal model theory, IMS GRADUATE SUMMER SCHOOL IN LOGIC, July 2022

I shall talk about modal model theory at the IMS Graduate Summer School in Logic at the National University of Singapore, 19th of July 2022. This will include results from my collaborative work with Joel David Hamkins as well as some new results of mine, from projects supervised by Joel David Hamkins. (Edited on March […]

British Logic Colloquium PhD day

I gave a short introductory talk on modal model theory for the British Logic Colloquium PhD day, taking place at 1st September 2021 as a part of the BLC Annual Meeting 2021 at Durham University. I explained the general idea and gave an update on the progress of my research, pointing out some new directions towards which […]

Modal model theory

This blog post from August 2019 now includes an update with regard to a result that is now revoked. Research has its ups and downs… I would like to share with you a brief description of what I have been doing at Oxford for the past eight months. Since my adviser has already written about […]

What complex numbers can tell us about the Multiverse?

There is an ongoing debate among mathematicians and philosophers on the nature of the realm where all mathematical activities are performed. But, before I pose the problem, we need to answer a pertinent question: “A realm? Do you mean like… our minds or what?” No. I mean metaphysical entity mathematicians are studying just like physicists […]