Monday 6.1.2025, 16:40 Department of Logic. For more details, see https://logika.ff.cuni.cz/en/research/seminar/. Ondrej Jezil (PhD student, MFF UK): Title „Forcing in Bounded Arithmetic: How to force a new natural number?“ Abstract: The field of bounded arithmetic studies the provability of $\Pi_1$ statements in weak subsystems of Peano Arithmetic, which are collectively known as theories of bounded arithmetic. The study of these systems is deeply connected to computational complexity and propositional proof complexity. In this talk, we will give an overview of the relevant theories and give a high-level explanation of how forcing is used to establish independence over them.