Talk:UTM theorem

I think we need a definition of $\varphi _{i}$ it isn't clear how this is defined. jbolden1517^Talk 21:06, 28 April 2009 (UTC)

An informal explanation (like "A Gödel number is a way to encode a program; a utm is an interpreter for such programs: it takes the Gödel number and executes the encoded program") would be great. The link "Gödel numbering" refers to an article about numberings of formulas, not of computable functions; in the latter sense, "Gödel numbering" is used in the Utm_theorem article, however. Moreover, the article defines φ_i to be a number, but then applies it to x∈N like a function. Maybe, i is the Gödel number and φ_i is the associated computable function? Last, not least, I wonder if the enumeration needs to be computable in some sense (I can't make this question more precise as long as a precise def. of Gödel number is missing). Maybe, the notion of Gödel numbering is not needed here at all; rather, programs should be given as Turing programs (sequence of quintuples), like in the referring article Turing_machine#Universal_Turing_machines? Jochen Burghardt (talk) 22:32, 14 June 2013 (UTC)