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A theory containing every sentence is trivial. Fundamental group, Van Kampen's Theorem, covering spaces. Entropy, harmonic functions, and Poisson boundary (following Kaimanovich-Vershik theory). Hilbert wanted: to formalize all mathematical reasoning into an exact notation with algorithmic rules; to provide axioms for all mathematical theories, such that no contradictions are provable (consistency), and all true facts are provable (completeness). As lions, tigers and bears roam lazily about Peru's largest zoo, archeologists are busy digging up stranger animals from the ground beneath them.
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Publisher: Thomson Learning; 2nd ed. edition (September 1, 2002)
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