Timeline for Confusion regarding the requirements for a recursive ordinal notation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4 at 14:26 | comment | added | Joel David Hamkins | Yes. You want to be able to computably decide the intended order, based only on the notations. | |
| Apr 4 at 14:20 | comment | added | mmiliauskas |
Do I understand correctly that what the second property requires is for an algorithm less to exist that less(Gödel number(ordinal_1), Gödel number(ordinal_2)) is the same as comparing ordinal_1 with ordinal_2?
|
|
| Apr 4 at 14:07 | vote | accept | mmiliauskas | ||
| Apr 4 at 14:06 | comment | added | mmiliauskas | Joel David Hamkins, thanks for your reply! It just dawned on me a sentence from the article I referred to "It is traditional and [...] common practice in computability theory to to restrict oneself to natural numbers as the inputs and outputs of algorithms" as I went for a walk :) Because of Gödel numbering one can think of f(x) mapping as mapping ordinal notations to ordinals <=> Gödel's number of ordinal notation to Gödel's number of ordinals <=> natural numbers to natural numbers. | |
| Apr 4 at 12:58 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 194 characters in body
|
| Apr 4 at 12:46 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 293 characters in body
|
| Apr 4 at 12:24 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |