I was reading about Hilbert's, Birkhoff's and Tarski's axioms of Euclidean geometry, and I am very curious to learn how do mathematicians know that these different axiom systems lead to the same "body of knowledge" (in this case, Euclidean geometry). Also, how do they know that every theorem of Euclidean geometry (or other field) can be proved with their system of axioms?
2026-02-24 01:44:32.1771897472
Different axioms for Euclidean geometry and other bodies of knowledge
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