The Ultimate Supercompactness Measure—Logic Advanced CLass, University of Oxford, June 2024

This will be a talk for the Logic Advanced Class at the Mathematical Institute, University of Oxford. The topic concerns the extension of the axiom of determinacy as well as the axiom . It will take place on the 13th of June 2024 at 11 AM in the lecture room C3. Abstract. Solovay defined the […]

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 […]

Resurrection Principles

This will be a talk for the IMS Logic Summer School at the National University of Singapore on the June 26th 2023. Abstract. The resurrection principle (RP) asserts that, in each forcing extension, all true assertions with real parameters retain their forceability throughout subsequent forcing extensions. This property exhibits deep connections with set-theoretic geology, the […]

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 […]

The tension between large cardinals and resurrection, Cambridge March 2023

I shall give a short talk about the tension between the strong axioms of infinity and resurrection. This time at the Set Theory in The United Kingdom meeting at the University of Cambridge, 7th of March 2023. If time permits, I shall sketch a proof of the failure of necessary -resurrection. Abstract. Usuba proved that the […]

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 […]

Usuba’s extendible and resurrection, IMS GRADUATE SUMMER SCHOOL IN LOGIC, July 2022

I shall talk about the tension between resurrection and large cardinals at the IMS Graduate Summer School in Logic at the National University of Singapore, 7th of July 2022. Abstract. The mantle is the intersection of all ground models of the universe. By a result of Usuba, the mantle is a ground in the presence of […]

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 […]