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Cantor's theorem, Woodin Cardinal, Sacks Forcing and Martin's Axiom are just some of well-known theorems and concepts of mathematics which have the name of those mathematicians who introduced these theorems and concepts for the first time. I think no reasonable mathematician calls his or her discovered theorem and concept using his or her own name at the first time. In fact after a while the mathematics community gives such names to theorems and concepts. Also there are many other new theorems and concepts which remain without any particular name.

Question: What are the main parameters which attach the name of a mathematician to his or her discovered theorem and concept? Any references in sociology of mathematics community about this phenomena is welcome.

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    $\begingroup$ This is only speculation, but I believe that a theorem gets the name of the discoverer (or rediscoverer) when a person cites them in their paper and chooses to do the honor of calling it "The theorem of Cantor" or "Cantor's Theorem". Then subsequent papers would refer to it in the same fashion until it has caught on enough that it falls into general knowledge. $\endgroup$ – Joel Jun 6 '14 at 13:55
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    $\begingroup$ The practice varies widely from field to field. At one extreme, some fields of mathematics attach proper names to concepts with abandon. At the other extreme, some fields of mathematics are very parsimonious with proper names, instead naming theorems with dry mathematical phrases. $\endgroup$ – Lee Mosher Jun 6 '14 at 13:57
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    $\begingroup$ "Well-known"?? But for Cantor's Theorem, which is known even to non-mathematicians, the other three seem to be rather very specialized , particular things in advanced set theory and logic $\endgroup$ – DonAntonio Jun 6 '14 at 13:59
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    $\begingroup$ @whoever edited the question to change "his" to "his or her": why not "his or her or its"? Why do you hate theorem-proving machines? You must be some kind of an -ist. $\endgroup$ – bof Jun 6 '14 at 14:14
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    $\begingroup$ See "Eponymy in Mathematical Nomenclature: What's in a Name and What Should Be" by Merwyn R. Henwood and Ivan Rival, for a forceful argument against the naming of mathematical concepts after persons, and in favor of descriptive names. $\endgroup$ – bof Jun 6 '14 at 14:22

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