1.While reading questions and answers on this forum, I read that the fact that Hilbert's axioms are built upon second-order logic is kind of disadvantage, but why ?
2.I heard that we can build coordinate system upon Hilbert's axioms, is it true ? And can we rigorously define it in other axiomatic systems of Euclidean geometry.
3. What are other disadvantages of Hilbert's axiomatic system and can we somehow create better axioms (I know there are others, but as I know they have their own disadvantages) ?
If this post has too many questions, say it in the comments and I will separate them into different posts.
Thanks in advance.
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Юрій Ярош
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You can see the post : what-is-the-modern-axiomatization-of-euclidean-plane-geometry. – Mauro ALLEGRANZA Apr 04 '18 at 17:32
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See also how-does-hilberts-axiomatization-relate-to-set-theory. – Mauro ALLEGRANZA Apr 04 '18 at 17:38
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@MauroALLEGRANZA Thanks. – Юрій Ярош Apr 04 '18 at 17:59