New models of $\sf{GL.3}$

Juan Pablo Aguilera^1
1 Vienna University of Technology

We discuss some new topological spaces which are sound and complete for the provability logic $\sf GL.3$ under suitable set-theoretic assumptions. One is the space of all ordinals with the normal-measure topology, assuming $\sf V$ is a “fine-structural” model of set theory. Another is the cardinal number $\aleph_{\varepsilon_0}$ with the closed-cofinal topology, assuming the Axiom of Determinacy. This is joint work with G. Stepanov.

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