Timeline for Does every set admit a ring structure or a field structure?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2023 at 3:04 | review | Close votes | |||
| Jul 21, 2023 at 3:05 | |||||
| Jul 14, 2023 at 12:57 | comment | added | YCor | It can quite important for such questions to specify the definition of a ring (associative? commutative? unital?) | |
| Jul 14, 2023 at 12:50 | comment | added | Timothy Chow | @JoelDavidHamkins It doesn't convey it explicitly, but I suspect that someone who says "every set up to cardinality" rather than "every set up to isomorphism" is probably thinking of the cardinal numbers $\aleph_0, \aleph_1, \ldots$ | |
| Jul 13, 2023 at 22:54 | comment | added | Joel David Hamkins | @TimothyChow How does "up to cardinality" convey AC? I suppose it would if you think of cardinalities as well-ordered, but ZF has a perfectly robust notion of cardinality without AC. And this is the notion that Peter is using. | |
| Jul 12, 2023 at 22:59 | comment | added | Timothy Chow | @PeterLeFanuLumsdaine I agree with your main point, but arguably, the phrase "up to cardinality" plays the role of communicating that the axiom of choice is being tacitly assumed. | |
| Jul 12, 2023 at 19:25 | comment | added | Peter LeFanu Lumsdaine | Just a side note: “…up to cardinality…” is redundant here, and essentially anywhere in mathematics one might say it. It means “…up to bijection…”, but algebraic structure obviously transfers along bijections, so it’s just the same as asking whether every set admits a field (etc) structure. // Relatedly, I’ve VTC’d: this question is off-topic here. It’s a good question, and would be fine on math.stackexchange, but it’s really not research-level — it could fit well as homework in a first or second course in logic. | |
| Jul 12, 2023 at 1:36 | history | became hot network question | |||
| Jul 11, 2023 at 18:03 | review | Close votes | |||
| Jul 12, 2023 at 9:20 | |||||
| Jul 11, 2023 at 17:45 | answer | added | Joel David Hamkins | timeline score: 24 | |
| Jul 11, 2023 at 17:42 | comment | added | Najib Idrissi | I'd be curious about a field structure on a set with six elements. | |
| Jul 11, 2023 at 17:41 | comment | added | Joel David Hamkins | Note: the axiom of choice is equivalent in ZF to the assertion that every nonempty set carries a group structure. mathoverflow.net/a/12988/1946 | |
| S Jul 11, 2023 at 17:35 | review | First questions | |||
| Jul 11, 2023 at 17:41 | |||||
| S Jul 11, 2023 at 17:35 | history | asked | Phthalo Johnson | CC BY-SA 4.0 |