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The Löwenheim-Skolem theorem for Gödel logic
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The number of axioms
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Determinate logic and the axiom of choice
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The omega-rule interpretation of transfinite provability logic
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The strength of infinitary Ramseyan principles can be accessed by their densities
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WKL0 and induction principles in model theory
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Universality, optimality, and randomness deficiency
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Evidence and plausibility in neighborhood structures
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Hyperations, Veblen progressions and transfinite iteration of ordinal functions
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Reverse engineering reverse mathematics