"::::::Of course everyone realizes that there's another article titled On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Perhaps this companion could absorb the ""history"" (including the problem of ""finitary"" proofs) and ""the aftermath"" (the immediate aftermath, am unclear where the ""contemporary"" aftermath should go) etc while the article associated with this page could be tightened to present explications of the theorems only. Per my comment above I encourage those who are interested mainly in the mathematical end of things (as opposed to the historical) and can lay their hands on it read Kleene's ""seven part"" explication in Volume I of Kurt Godel Collected Works.

(On different note, the ""Chinese remainder theorem"" comes up in some (but not all) of the explications. I did a search of our article and found no mention of ""chinese"" or ""remainder"". But when I searched wikipedia I discovered an article Gödel numbering for sequences that contains a detailed discussion of this topic. And here I thought he was relying on the fundamental theorem of arithmetic . . .. What's going on? And, is it just me or is there little or no coordination between these various-but-associated articles?) Bill           

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