Timeline for What is the theory of the random poset?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 30, 2021 at 15:00 | vote | accept | Keshav Srinivasan | ||
| Mar 30, 2021 at 14:10 | history | became hot network question | |||
| Mar 30, 2021 at 10:58 | comment | added | Gerald Edgar | Definition ... en.wikipedia.org/wiki/Fraïssé_limit | |
| Mar 30, 2021 at 8:21 | comment | added | Emil Jeřábek | The form of the axioms of the random graph is not $\Pi^0_2$, but $\forall_2$. The notation $\Pi^0_2$ means universal quantifiers followed by existential quantifiers followed by a formula using bounded quantifiers, allowing second-order parameters. This only makes sense in the language of arithmetic. The language of random graphs includes neither bounded quantifiers nor set parameters. | |
| Mar 30, 2021 at 8:09 | comment | added | Keshav Srinivasan | @JamesHanson I’m talking about the quantifier complexity of the sentences belonging to a certain set of sentences (called E_i,j by Wikipedia), a set which implies the theory of the random graph. | |
| Mar 30, 2021 at 8:07 | comment | added | James E Hanson | What do you mean when you say the random graph has a $\Pi^0_2$ axiomatization? Are you talking about the quantifier complexity of the sentences themselves or the computational complexity of the set of axioms? | |
| Mar 30, 2021 at 7:43 | answer | added | Emil Jeřábek | timeline score: 10 | |
| Mar 30, 2021 at 7:11 | comment | added | Emil Jeřábek | @TomaszKania As far as I can see, the class of finite rigs does not have a Fraïssé limit, as it lacks the joint embedding property (you can’t embed two rigs of different characteristics in a single rig). | |
| Mar 30, 2021 at 6:31 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 30, 2021 at 6:23 | comment | added | Tomasz Kania | Is there a random ring too? (Fraisse limit of finite rigs; should be okay as push-outs of finite rings are finite; if so, does it have a concreteish description?) | |
| Mar 30, 2021 at 6:05 | history | asked | Keshav Srinivasan | CC BY-SA 4.0 |