In this video, I discuss the history of the Entscheidungsproblem (the decision problem) and some of its partial solutions. This includes a description of Gödel numbering and some notes on whether zero should be considered natural.
Here's a good place to get started reading about the history of the entscheidungsproblem:
https://plato.stanford.edu/entries/church-turing/decision-problem.html
Wikipedia is also a good resource and includes a listing of known partial solutions to the entscheidungsproblem. Remarkably it seems like the boundary is precisely understood on the axis of quantifier prefixes!
https://en.wikipedia.org/wiki/Entscheidungsproblem
You can read more about Matrix's life and work on Wikipedia: https://en.wikipedia.org/wiki/Irving_Joshua_Matrix
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Solution to the Entscheidungsproblem through Numero-Logical Methods | NatokHD