## Formal Theories of Truth

**Ali Enayat**

*Department of Philosophy, Linguistics, and Theory of Science*

*University of Gothenburg, Sweden*

**Abstract**. The origins of the area known as Formal/Axiomatic Theories of Truth can be found in Tarski's groundbreaking investigations in the first half of the twentieth century, and particularly his explication of the notion of "truth in a structure'', and his famous theorem about undefinability of truth. The area has been actively investigated both by mathematical and philosophical logicians, using advanced methods, especially those from model theory and proof theory. The aim of the course is to introduce the audience to the general concepts, questions, results, techniques, and literature of the subject, as expounded in the recent excellent expositions in the books Axiomatic Theories of Truth by Volker Halbach (2015), and The Epistemic Lightness of Truth (2017), by Cezary Cieśliński.

**Language**: Persian, but the slides will be in English.

**Prerequisites**: The rudiments of Mathematical Logic, approximately at the level of Dr. Ardeshir's textbook منطق ریاضی, and basic familiarity with Gödel's incompleteness theorems.

**Recommended Readings Before the Course**:

- Axiomatic Theories of Truth, Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/truth-axiomatic/
- Tarski's Truth Definitions, Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/tarski-truth/

## Forcing Method

#### Mohammad Golshani*, Rahman Mohammadpour**

*School of Mathematics, Institute for Research in Fundamental Sciences (IPM)

**Institut für Diskrete Mathematik und Geometrie, TU Wien

**Abstract**. Our aim in this mini-course is to present a gentle introduction to the method of forcing, of which our presentation will be accompanied by many examples, explanations and justifications of used terms. We will be teaching the materials very smoothly and in a fashion that the participants are then able to perceive the crux of the forcing method. In particular the first session will be devoted to experiencing some easy concepts related to partially ordered sets. We intend then to focus on a detailed proof of the independence of Continuum Hypothesis from ZFC.

**Prerequisites**: To follow this mini-course, it would be convenient for the participant to have very basic knowledge of certain fundamental aspects of classical logic (e.g., formal proofs, structures and elementary substructures, consistency, Gödel’s completeness and incompleteness theorems) and basic axiomatic set theory, as well.

## Duality theory

#### Nick Bezhanishvili

Institute for Logic, Language and Computation (ILLC)

University of Amsterdam

**Abstract**. In this tutorial I will discuss Stone, Priestley and Esakia dualities for Boolean algebras, distributive lattices and Heyting algebras, respectively. I will also give a few examples of applications of these dualities. In particular, I will show how to obtain a characterization of profinite Heyting algebras using these dualities.

**Prerequisites**: There are no prerequisites except for mathematical maturity and all the necessary concepts will be defined in the course. However, some familiarity with the basic notions of topology might be helpful.

## Functional Interpretations

#### Paulo Oliva

School of Electronic Engineering and Computer Science

Queen Mary, University of London (QMUL)

**Abstract**. Functional interpretations provide us with a systematic way of translating logical dependencies into functional dependencies. The most well-known such interpretations include Kleene’s realizability, Kreisel’s modified realizability and Gödel’s Dialectica interpretation. In this series of lectures we will cover the basic concepts behind such functional interpretations, looking at each interpretation individually and then identifying the common features between them. We will also discuss the foundational motivations for the development of such interpretation as well as its more recent applications to program extraction from proofs and proof mining.

**Prerequisites**: Some familiarity with formal logic and axiomatic systems, in particular with natural deduction systems for propositional and predicate logic, is desirable.