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Q. You have asked about recursively denumerable sets on the SeT page. I am not sure if you are questioning: * 1). the existence of such a sets. * 2). whether such sets are well-defined *AND MORE IMPORTANT * 1). If you are tryimg to illicit more content, please feel free to add content to the page. * 2). If you are referring to the paradoxes resulting from looking at sets like X = {x: x is a set}, a more limited problem, Russell's Paradox is on the SetTheory page. In conclusion, perhaps an example of such a set would help. RoseParks Someone wrote "We require that sets be well-defined. Given an object Sn, we must be able to determine if Sn belongs to S." My point is simply that for most people doing set theory (I don't know who We is), this is not true. We do not require that, given an object, we are able to determine whether it is in a given set or not. Most people doing set theory do not, for example, claim that recursively enumerable sets which are not recursive do not exist. For example, the set of theorems of a given first order theory is very often only a semi-decidable set. Philosophically, some people may object to the claim that such sets exist, but it is not the usual position. -- CalvinOstrum Thank you Mr. Ostrum. With your permission, I will edit the SeT page and add your remarks. Or perhaps you would like to add to the page yourself? I am a teacher of Math at the University level, but no expert on Set Theory. I was simply adding a definition, apparently none too carefully. RoseParks |
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