In mathematical proof,we usually create a function based on the formula like "∀x∃!yR(x,y)" just in the natural language. However, how could we express this process in the first-order language? And,haven't the function already been specified in symbol library?If so,how can we create a new function?
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https://en.m.wikipedia.org/wiki/Extension_by_definitions – Mark Saving Jan 28 '23 at 04:11
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Thanks a lot.It does help. – Fore Blue Jan 28 '23 at 09:38
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See also Understanding Extension by definition – Mauro ALLEGRANZA Jan 30 '23 at 08:00
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another way to give new names is the $\iota$-operator of definite descriptions which you may add conservatively to first order logic – Nico Feb 26 '23 at 22:14