Modal graph theory as a foundation of mathematics

This will be a talk for the Barcelona Set Theory Seminar, 17 March 2021 4 PM CET (3 PM UK, 4 PM Poland). I understand the talk will be held on Zoom; please contact Claudio Ternullo for access. Abstract. One can consider the class of all graphs as a Kripke model of possible worlds, where […]

Playing with pebbles on the multiverse

Please find a recording below of a mini-talk I gave during Set Theory in The United Kingdom @ Home on December 4, 2020. We generalize Ehrenfeucht–Fraïssé games from classic model theory to modal model theory with actuality. Please note that it has come to my attention during the talk that Sam Adam-Day had considered modal […]

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 […]

Chaos does not always prevail

One of the first astonishments I faced as an undergraduate mathematics student was that chaos prevails. What do I mean by that? Well, there are more irrational numbers than rational numbers, there are more non-computable functions than computable, and, finally, there are more continuous functions devoid of a derivative than those which have one. In the […]