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Full Idea
A set is 'effectively enumerable' if an (idealised) computer could be programmed to generate a list of its members such that any member will eventually be mentioned (even if the list is empty, or without end, or contains repetitions).
Gist of Idea
A set is 'effectively enumerable' if a computer could eventually list every member
Source
Peter Smith (Intro to Gödel's Theorems [2007], 02.4)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.15
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |