Timeline for Arguments against large cardinals
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 2 days ago | comment | added | Mikhail Katz | What kind of counterexample in topology is caused by measurable cardinals? | |
| Jan 10, 2019 at 9:19 | comment | added | SSequence | "Ordinal notation systems ... give us a well-understood picture of how a theory operates, which (among many other benefits) counteracts doubts about consistency." Very nice point. Even though I am pretty much ignorant of the subject, I find it a bit surprising that logicians studying these topics don't seem to mention this in a clear manner (like in quoted sentence for example) frequently enough. But again, perhaps I haven't read enough. | |
| Jan 8, 2019 at 18:50 | comment | added | Dmytro Taranovsky | @JamesHanson While all models satisfying basic arithmetical axioms are infinite, there are finite structures that resemble models and for which we get an analog of Gödel's completeness theorem: no inconsistency of length $N'$ $\implies$ quasimodel good enough for statements of length $N$ $\implies$ no inconsistency of length $N$. There are different formalizations of this (and different notions of quasimodels), but one notion is in Finite Analogues of Infinite Structures. | |
| Jan 8, 2019 at 17:40 | comment | added | James E Hanson | What is a 'quasimodel'? | |
| Jan 8, 2019 at 4:21 | history | answered | Dmytro Taranovsky | CC BY-SA 4.0 |