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 theory of the category of sets

This was a talk for the Junior Logic Seminar at the University of Oxford, 7th of June 2022. Abstract. I shall investigate the modal theories and validities in a variety of cases arising from the archetypical concrete category of sets and functions. I introduce new insights into the method of control statements, answering a MathOverflow […]

The Mathematical Multiverse

I shall speak about some recent developments on the subject of modal model theory for the Junior Logic Seminar at the University of Oxford. The talk, titled The Mathematical Multiverse, will take place at the Mathematical Institute on November 16, 2021 at 5PM UK time. Please contact Brian Tyrrell should you like to join us. […]

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 […]

Think you have a choice? Vitali’s revenge

I learned a fascinating fact a few weeks ago at the Philosophy of Mathematics, graduate lecture seminar at the University of Oxford. That week’s discussion was led by Professor Hamkins and concerned a remarkable book Defending the Axioms: On the Philosophical Foundations of Set Theory written by Penelope Maddy, logic and philosophy of science Distinguished […]

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 […]

Liar’s Paradox

This was a talk for “Academic English: Spoken Communication 2” that I gave last Thursday. Please note that this presentation was aimed for non-mathematicians and non-philosophers. Thus, I concealed any anxiety about the topic for clarity’s sake. There is a short clip on the second slide and a GIF on the third one. Unfortunately, these […]

University of Oxford

I shall take up a place as a Recognised Student in the Faculty of Philosophy at the University of Oxford starting 7th January 2019. I shall be undertaking research on the topic of “the philosophical consequences of recent advancements in ‘Multiverse inspired mathematics.” My academic adviser will be Professor Joel David Hamkins. I anticipate this […]