Expressibility and Incompleteness

About this programme

No fees are charged for EU and EEA citizens, Swedish residence permit holders and exchange students. How powerful is logic – and where are the limits of what can be expressed and proved? In the course Expressibility and Incompleteness, you will explore some of the most fascinating questions in modern logic. You will delve into intuitionistic logic and second-order logic, examining how different logical systems shape what we can express, prove, and know. A central part of the course is Gödel’s famous incompleteness theorems, which reveal fundamental limits to what can be proved within formal mathematical systems. You will gain an understanding of the ideas behind these groundbreaking results while working with their proofs, applications, and consequences. The course is ideal for students who want to deepen their knowledge of formal logic and develop a sharper understanding of the relationships between language, proof, truth, and the limits of mathematics. Admission to the course requires Logic and completeness (LOG112) or equivalent. In addition, language proficiency equivalent to English 6 is required. Selection is based upon the number of credits from previous university studies, maximum 165 credits. The Faculty of Humanities is located in the Humanisten building at Renströmsgatan 6. The Department of Philosophy, Linguistics and Theory of Science has its premises on the 5th floor. Both the Faculty of Humanities and the adjacent Humanities Library offer several study areas and group rooms.