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lawrencecpaulson.github.io | ||
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www.cs.uic.edu
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math.andrej.com
[AI summary] The discussion revolves around the interpretation of inductive types and their elements in type theory, particularly focusing on the concept of 'reachability' through constructors. The key points include: 1) The idea that inductive types may have elements that are not reachable by constructor application, which is a non-absolute property. 2) The distinction between internal and external perspectives in models, where the 'standard' natural numbers (N) in a model may differ from the meta-theoretical N. 3) The role of exotic models in highlighting the non-absoluteness of inductive types and their elements. 4) The importance of recognizing that inductive types are not freely generated, as seen in identity types, and the challenges of defining genera... |
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www.themathdoctors.org
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aeon.co
Some have thought that logic will one day be completed and all its problems solved. Now we know it is an endless task |
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