Timeline for Why are model theorists free to use GCH and other semi-axioms? [closed]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2016 at 11:22 | history | closed |
Włodzimierz Holsztyński Steven Landsburg András Bátkai Stefan Kohl♦ Marco Golla |
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| Oct 9, 2016 at 2:03 | comment | added | Steven Landsburg | How can one philosophically justify the use of the commutativity axiom in abelian group theory? | |
| Oct 9, 2016 at 1:25 | answer | added | Alex Kruckman | timeline score: 10 | |
| Oct 8, 2016 at 22:52 | review | Close votes | |||
| Oct 9, 2016 at 11:22 | |||||
| Oct 8, 2016 at 22:20 | answer | added | arsmath | timeline score: 0 | |
| Oct 8, 2016 at 22:15 | comment | added | Andrés E. Caicedo | There are many papers in model theory where the main difficulty is in removing GCH-like assumptions from some arguments. As François indicates, the main use of the hypothesis is to simplify matters. One can later see what can be done without invoking it, and what results in a genuinely independent statement. | |
| Oct 8, 2016 at 20:44 | comment | added | François G. Dorais | The main use of GCH is that it resolves all of cardinal arithmetic, even in the singular cases. Since cardinality computations arise often in model theory, not always in interesting ways, assuming GCH is a good way to focus on the main subject and sweep away distractions. Another motivator is that GCH facilitates some transfinite constructions involving diagonalization. I'd be very surprised if the authors thought of the hypothesis as statement regarding foundational belief. | |
| Oct 8, 2016 at 20:30 | comment | added | Wojowu | You don't need to believe in GCH in order to investigate a question of the form "does GCH imply...?". | |
| Oct 8, 2016 at 20:22 | history | asked | user99445 | CC BY-SA 3.0 |