Workshop overview
We are pleased to propose a workshop that aims to bring together researchers interested in exploring applications of algebra-valued models to philosophical issues. Boolean-valued models, were initially introduced by Dana Scott, Robert M. Solovay, and Petr Vopenka in the 1960s to provide a simplified account of independence proofs. Since then, the construction of Boolean-valued models has been extended to various logical environments, resulting in a diverse range of non-classical models of set theory.
This workshop seeks to highlight the recent application of algebra-valued models to sharpen our understanding of philosophical, set-theoretic, and logical notions. Notable advancements include the study of arbitrary objects, logical connectives, mereological vagueness, iterative notions of set, and model- theoretic notions. Building upon these achievements, our workshop aims to expand this research trend by exploring philosophical concepts such as intensional entities, higher-order set theories and set-theoretic pluralism.
Cofirmed speakers
- Giorgio Venturi (University of Pisa)
- Sourav Tarafder (St. Xavier's College, Kolkata)
- Leon Horsten (University of Konstanz)
- Neil Barton (University of Oslo)
- Ethan Brauer (University of Oslo)
- Paul Gorbow (University of Stockholm/University of Oslo)
Programme
Day 1: 9th of November (Niels Henrik Abel's house: Room 400)
- 10.00 - 11.15 Sourav Tarafder: A road to non-classical models of set theory
(1 hour + 15 minutes) - 11.15 - 12.30, Neil Barton: Potentialist sets, intensions, and non-classicality
(1 hour + 15 minutes) - 12.30-13.15 Lunch
- 13.15-14.30, Leon Horsten: Boolean-valued sets as arbitrary objects
(1 hour + 15 minutes) - 14.30-16.00 Panel Session on Algebra-valued models and pluralism Moderator: Giorgio Venturi
Day 2: 10th of November (Georg Morgenstiernes Hus: Room 452)
- 10.00-11.15, Giorgio Venturi: On Independence in non-classical Set theory
(1 hour + 15 minutes) - 11.15-12.30, Ethan Brauer : A Model of Height and Width Potentialism
(1 hour + 15 minutes) - 12.30-13.15 Lunch
- 13.15-14.30, Paul Gorbow : Algebraic New Foundations
(1 hour + 15 minutes) - 14.30-16.00 Panel Session: Intensional entities and algebra-valued models Moderator: Neil Barton
- 18.00 Conference Dinner at Tekehtopa
Summaries
Leon Horsten: Boolean-valued sets as arbitrary objects
I explore the connection between boolean-valued class models of set theory and the theory of arbitrary objects in roughly Kit Fine’s sense of the word. In particular, I explore the hypothesis that the set theoretic universe as awhole can be seen as an arbitrary entity. According to this view, the set theoretic universe can be in many different states. These states are structurally like boolean-valued models, and they contain sets conceived of as variable or arbitrary objects.
Ethan Brauer: A Model of Height and Width Potentialism
Using the idea of a lawless sequence—which comes from intuitionistic anal- ysis and which has recently been given a potentialist treatment—I develop a model of set theory that combines height potentialism and width potentialism. I will discuss the relation of this model to forcing potentialism, multiverse views of set theory, and the iterative conception of set.
Sourav Tarafder : A Road Towards models of non-classical set theories
Non-classical set theories grapple with challenges pertaining to the existence of their models. In the course of this presentation, we will expound upon a method for generating models within the realm of non-classical set theories. Building upon the groundwork laid by Boolean-valued models in classical set theory, we will extend our approach to crafting algebra-valued models for non- classical set theories. Within these models, we will delve into several instances of independence results, shedding light on the intriguing interplay of mathematical concepts. Additionally, we will embark on an exploration of cardinal arithmetic, uncovering pivotal theorems that illuminate the cardinality of sets. The presen- tation will culminate in an examination of a handful of open questions, inviting further contemplation and discussion on the subject matter.