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math.LO2020
Positive logics
Saharon Shelah, Jouko Väänänen
Lindström's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. If we do not assume that logi…
math.LO2020
Inner Models from Extended Logics: Part 1
Juliette Kennedy, Menachem Magidor, Jouko Väänänen
If we replace first order logic by second order logic in the original definition of Gödel's inner model , we obtain HOD. In this paper we consider inner models that arise if we…
math.LO2020
Inner Models from Extended Logics: Part 2
Juliette Kennedy, Menachem Magidor, Jouko Väänänen
We introduce a new inner model arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively , the regular uncountable…