Logic at GU
Welcome to the webpage of the logic group at the University of Gothenburg. Information about our research and activities can be found through the links to the left. More detailed information is available through the personal pages of group members and our homepage at the University of Gothenburg.
Boole, Tarski, Stone, Lawvere, Reyes, Makkai
We prove that \(\omega^2\) strictly bounds the iterations required for modal definable functions to reach a fixed point across all countable structures. In doing so, we both extend and correct the previously claimed result on closure ordinals of the alternation-free \(\mu\)-calculus. The new approach sees a reincarnation of Kozen’s well-annotations, originally devised for showing the finite model property for the modal \(\mu\)-calculus. We develop a theory of conservative well-annotations where minimality of the annotation is guaranteed, and isolate relevant parts of the structure that necessitate an unfolding of fixed points. This adoption of well-annotations enables a direct and clear pumping process that rules out closure ordinals between \(\omega^2\) and the limit of countability.