Timeline for Forcing and new ordinals
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2019 at 19:28 | history | edited | Thomas Benjamin | CC BY-SA 4.0 |
added more information for clarification
|
| Nov 16, 2019 at 17:41 | comment | added | Thomas Benjamin | The last two sentences in the previous comment should read: It would certainly be great if either of you could. Thanks in advance for your help. | |
| Nov 14, 2019 at 0:44 | comment | added | Thomas Benjamin | (cont.) models here), certainly is a sense of the phrase, "which in turn are determined by which ordinals are in $M$. What would be more interesting is providing a proof that adding new (imaginary?) ordinals to the model you speak of in your example will recover $V$ = $L$. Can you and/or Prof. Blass do this? It would certainly if either of you could. Thanks in advance for hour help. | |
| Nov 14, 2019 at 0:37 | comment | added | Thomas Benjamin | @NoahSchweber: You are correct in your statement, "we can have models with the same ordinals but with different sets of ordinals (and the example you gave is great as well!), but I think that you and Prof. Blass, and I, are talking at cross purposes here. The phrase I used, "which in turn are determined by which ordinals are in $M$", has different senses, and you and Prof. Blass chose one sense, and I another. The sense I used , namely, that the ordinals in $M$ form the basis from which $P^{M}$ forms the other sets of ordinals (let us assume, for the sake of argument, that we are using set | |
| Nov 13, 2019 at 3:28 | comment | added | Noah Schweber | @ThomasBenjamin You wrote that the sets of ordinals in $M$ are determined by the ordinals in $M$. But that's not true: we can have models with the same ordinals but with different sets of ordinals. (E.g. if $M$ is any model of ZFC + $\neg$V=L, then $M$ and $L^M$ have the same ordinals but have different sets of ordinals.) | |
| Nov 12, 2019 at 22:39 | comment | added | Thomas Benjamin | @AndreasBlass: Although you are certainly correct in stating that "Two transitive models of $ZFC$ with the same ordinals need not have the same sets of ordinals", I am unclear why my added statement, "which in turn is determined by which ordinals are in $M$" ('is should be replaced by 'are' in that statement) should imply that models of $ZFC$ having the same ordinals should have the same sets of ordinals. Nevertheless, I have removed the offending "added comment" and placed it where it hopefully won't cause me any problems. | |
| Nov 12, 2019 at 22:27 | history | edited | Thomas Benjamin | CC BY-SA 4.0 |
removed added comment where it shouldn't be and placed it where it should be, and added a parenthesis where it should be as well
|
| Nov 12, 2019 at 1:40 | comment | added | Andreas Blass | Your added comment, "which in turn is determined by which ordinals are in $M$," is wrong. Two transitive models of ZFC with the same ordinals need not have the same sets of ordinals. | |
| Nov 11, 2019 at 22:06 | history | edited | Thomas Benjamin | CC BY-SA 4.0 |
Corrected spelling mistake.
|
| Nov 11, 2019 at 22:00 | history | answered | Thomas Benjamin | CC BY-SA 4.0 |