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  • Zuzana Haniková: Theory of finite sets and Peano arithmetic (Feb 22, 2024 - March 7, 2024)

    This minicourse is based on Kaye and Wong's paper "On Interpretations of Arithmetic and Set Theory". It concerns the Ackermann's interpretation of the theory of hereditarily finite sets in PA and the role of some set theory axioms in it. We will also revisit some material related to Vopěnka's Alternative set theory, where similar phenomena were observed.

    First talk slides: pa_zffin.pdf.
    Second talk slides: pa_zffinII.pdf
    Third talk slides: pa_zffinIII.pdf

    The slides give a guide to the remaining reading material.

  • Chris Lambie-Hanson: Well-orderings in logic and mathematics

    Though not as glamorous as some of its relatives, the notion of well-ordering is arguably one of the most important and useful ideas in mathematical logic and set theory, lying at the heart of a number of important breakthroughs over the last 150 years. We will survey the valuable role that well-orderings and the Well-Ordering Theorem have played in the development of the modern foundations of mathematics and in applications of logic and set theory to other areas of mathematics. We will cover over 100 years of research, from the late 19th century to the present day, along the way investigating the roles that well-orderings play in connection with constructions of pathological mathematical objects, infinitary logics, questions of definability, large cardinals, and infinite games.