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When you hear the words Alzheimer's disease, what do you think of? The truth is, the picture most of us have of the disease is incomplete. Alzheimer's disease doesn't start when someone starts to lose their memory. It actually starts years – sometimes decades – earlier. The Rethinking Alzheimer's Disease Podcast is an engaging, narrative-style podcast miniseries for those curious or motivated to learn about Alzheimer’s disease. Perhaps you have a family member with Alzheimer’s disease, or ca ...
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Helmut Schwichtenberg (LMU) gives a talk at the MCMP Colloquium (5 December, 2013) titled "Remarks on the foundations of mathematics". Abstract: We consider minimal logic with implication and universal quantification over (typed) object variables. Free type and predicate parameters may occur. For mathematics we need (i) data (the Scott - Ershov partial continuous functionals) and (ii) predicates (defined inductively or coinductively). In this setting we can define (Leibniz) equality, falsity and the missing logical connectives (negation, disjunction, existential quantification, conjunction). Ex-falso-quodlibet can be proved. Using Kreisel's (modified) realizability we can (even practically) extract computational content from proofs, and (internally) prove soundness.
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