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The Helsinki Logic Group

Mathematical logic uses exact mathematical methods, originally developed in algebra, topology, measure theory, analysis, and combinatorics to study the two thousand year old subject of logic. During the 20th century, thanks to the revolutionary results of Gödel, but also of Skolem, Gentzen, Church, Turing and Cohen, mathematical logic developed into a deep research area with applications to philosophy, computer science, linguistics and, indeed, mathematics itself. In mathematical logic the Helsinki Logic group focuses on set theory, set-theoretic model theory, model theory, finite model theory, dependence and independence logic, second order logic, as well as the history of logic and foundations and philosophy of mathematics. The group has developed methods in infinitary logic involving transfinite games and trees to investigate the structure of uncountable models, with connections to stability theory. The group is also known for its work in generalized quantifiers: their hierarchies, their applications in linguistics and computer science, and their set-theoretical properties, as well as for its work in the theory of abstract elementary classes and metric model theory. A recent topic of interest is dependence logic, a project to develop the mathematics and logic of dependence and independence concepts, as they are used in mathematics, computer science and elsewhere.

 


Advanced Course May 14-17, 2018, C122, 14-16: Mirna Dzamonja

Title: "Forcing, forcing axioms and a hope for having them at cardinals other than aleph_1"

Abstract: We start with some history and some constructions toward the singular cardinal hypothesis. We then move to more recent ground, mentioning some known forcing axioms. We conclude with the line of our work in a series of papers with various co-authors (including Cummings, Komjath, Magidor, Morgan and Shelah) on forcing at the successor of a singular cardinal.

Seminars

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