Timeline for The sets in mathematical logic
Current License: CC BY-SA 3.0
27 events
| when toggle format | what | by | license | comment | |
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| Mar 25 at 22:08 | comment | added | Joe | @TheMathemagician, were you able to track down Elliot Mendelson? | |
| S Mar 10 at 19:26 | history | suggested | C7X |
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| Mar 10 at 18:41 | review | Suggested edits | |||
| S Mar 10 at 19:26 | |||||
| Jan 26, 2019 at 15:51 | comment | added | user21820 | For example, semantic-completeness for countable first-order theories does not need AC, but in general you would need a well-ordering of the language. ACA can deal with countable languages easily, so it is incorrect to think that anything near ZFC is needed for basic theorems about logic. I give in this post a brief sketch of what assumptions we need in order to build things non-circularly. @PiotrPstrągowski: You may also be interested in my comments. | |
| Jan 26, 2019 at 15:45 | comment | added | user21820 | @TimCampion: ACA (a very weak subsystem of second-order arithmetic) is sufficient to prove a lot of concrete mathematical theorems, including most theorems about concrete formal systems (which are necessarily syntactic systems involving only finite strings over a finite alphabet). The problem with many logic texts is that they use ZFC as the meta-system and hence push the theorems to their maximum generalization in the ZFC world, such as for uncountable languages. This is obviously irrelevant to the real world. | |
| Sep 26, 2012 at 18:08 | comment | added | Piotr Pstrągowski | I don't know how it's even possible I didn't see this question until today! I remember asking this over and over again. | |
| Feb 17, 2012 at 18:02 | answer | added | user16974 | timeline score: 0 | |
| Feb 17, 2012 at 14:27 | answer | added | Buschi Sergio | timeline score: 0 | |
| Feb 17, 2012 at 8:41 | answer | added | The Puzzled Logician | timeline score: -2 | |
| Apr 25, 2011 at 20:49 | comment | added | Dan Piponi | What is the chain of reasoning that is circular? I'm hoping to see answer of the form A→B→C→…→A. | |
| Apr 25, 2011 at 15:17 | answer | added | Brendan Cordy | timeline score: 7 | |
| Apr 25, 2011 at 9:00 | vote | accept | zzzhhh | ||
| Apr 24, 2011 at 21:44 | comment | added | Tim Campion | This sort of question might not be addressed in a standard text on mathematical logic, but I HOPE it's addressed in texts on metamathematics? The only one I've heard of is Kleene's Metamathematics, but I have no idea if this or any other book explicitly addresses these issues... Perhaps some philosopher in the room might be able to weigh in? | |
| Apr 24, 2011 at 21:11 | comment | added | The Mathemagician | I think this is a wonderful simple question and it shows that questions about the foundations of mathematics cannot really be formulated independently of metaphysical questions.I'm going to track down Elliot Mendelson in retirement,ask him what he thinks about this question and then get back to you. | |
| Apr 24, 2011 at 20:19 | answer | added | Timothy Chow | timeline score: 13 | |
| Apr 24, 2011 at 18:40 | answer | added | kakaz | timeline score: 0 | |
| Apr 24, 2011 at 18:19 | comment | added | Michal R. Przybylek | Amit: You have to be more careful - a set of sets in the sense of second-order quantification is an "outer" set of "inner" sets. Such an "outer" set does not need correspond to any "inner" one. | |
| Apr 24, 2011 at 18:06 | comment | added | Amit Kumar Gupta | @Thierry, in set theory, everything is a set, so whether we're quantifying over sets, or over sets of sets, or sets of sets of sets, etc. these are all first-order quantifications. | |
| Apr 24, 2011 at 17:15 | comment | added | Thierry Zell | I don't understand your axiom of extensionality example. What makes it first order, if it begins with $\forall A B$? | |
| Apr 24, 2011 at 15:31 | answer | added | Sergey Melikhov | timeline score: 7 | |
| Apr 24, 2011 at 14:43 | answer | added | Michal R. Przybylek | timeline score: 4 | |
| Apr 24, 2011 at 14:34 | comment | added | Sergey Melikhov | @Gerald Edgar: Did you have any particular book in mind? If yes, why not reveal it? | |
| Apr 24, 2011 at 13:27 | comment | added | zzzhhh | @Harry Altman. Yes, they are distinct, but this is not my main concern. | |
| Apr 24, 2011 at 13:12 | comment | added | Harry Altman | You mean "circularity", not "paradox". These are distinct notions. | |
| Apr 24, 2011 at 13:04 | answer | added | Stefan Geschke | timeline score: 45 | |
| Apr 24, 2011 at 12:36 | comment | added | zzzhhh | I have read serveral basic textbook on mathematical logic, but none of them answers my question successfully. | |
| Apr 24, 2011 at 8:57 | history | asked | zzzhhh | CC BY-SA 3.0 |