Fundamental Theorem Of Logic

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Two major results related to Hilbert second problem:
(1) Kurt Gödel's Incompleteness Theorems
(2) James Kuodo Huang's Fundamental Theorem of Logic


Fundamental Theorem of Logic.
Any sound consistent logic system is complete in the Hilbert logic systems containing it.


What the fundamental theorem of logic has proved can be explained to everyone as follows:
If any goal is true, then people can use their human logical mind and their logical methods and technology to reach this goal in the finite future days. For instance, today's "Open AI" possible to be done in the near future if it is truly possible.

For details, please refer to James Kuodo Huang's publications and talks from 2005-2025.
In order to understand the theory and proof of the Hilbert logic systems, you probably need to be a mathematician. However to use Hilbert logic systems (AKA Hilbert complete perfect logic systems), all you need to know intuitively the Boolean logic theory and some basic mathematics. Therefore all engineers, scientists, and well-trained college students have applied the Hilbert logic systems without knowing it.
To build reliable AI related systems, Hilbert logic system's technology is a good one.