In addition to the points made in our How to ask a good question? page, I feel that questions here should be as self-contained as possible. I generally take this to mean that an "expert" in the question's main tag (set-theory, for the example question) should be able to fully and unambiguously understand — and answer, if applicable — the question without looking at any additional sources (be they websites, texts, videos, or research articles).
Links to such sources are of course valuable, but as secondary material. The question should be intelligible without following them.
With this criteria, the question
I don't understand the statement "both $T$ and $A$ belong to $L_{\omega_2}$" at page 12 of this paper.
fails miserably. It's impossible to discern what the objects $T$ and $A$ (and possibly even $L_{\omega_2}$) are without following the link.
I would argue that
I am self studying this paper by T. Jech on Trees. At pages 11-12 he proves that if $V=L$ then there exists a Suslin tree. The construction of the Suslin tree $T$ proceeds as usual by induction on levels, but the induction step is not trivial. At page 12 he claims that $T$ belongs to $L_{\omega_2}$. I can't understand why this is true. In fact, I believe this follows from some specific properties of the constructible universe (and more precisely of $L_{\omega_2}$) together with some absoluteness argument. But the inductive definition is rather complex, hence I don't know where to start to show this.
also doesn't pass muster, as answerers will likely still have to read the linked paper. (IMHO, the answer relies on more details of the construction of $T$ than appear in this version.)
Better still is a question like the following:
I have been reading
- Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1--14, MR284331.
On pages 11-12 he constructs a (normal) Suslin tree $T$ in the constructible universe $L$. At one point in the proof he states that $T$ belongs to $L_{\omega_2}$, but I don't see why this is true. I believe this follows from some specific properties of the constructible universe (and more precisely of $L_{\omega_2}$) together with some absoluteness argument.
In more detail, $T$ is constructed by recursively constructing its levels $U_\alpha$ ($\alpha < \omega_1$). The elements of $T$ are taken to be countable ordinals. Given $U_\alpha$ it is "obvious" how to construct $U_{\alpha+1}$. The construction of $U_\alpha$ for limit $\alpha < \omega_1$ is as follows.
There exists a function $f : \omega_1 \to \omega_1$ such that for each $\alpha < \omega_1$, $$ \langle L_{f(\alpha)} , \mathord{\in} \rangle \models \alpha\text{ is countable}$$ (i.e. there exists $g \in L_{f(\alpha)}$ which maps $\omega$ onto $\alpha$). We choose such a function $f$ and for every limit ordinal $\alpha$ we construct $U_\alpha$ such that we kill all maximal antichains in $T | \alpha \; [ = \bigcup_{\beta < \alpha} U_\beta ]$ which are in $L_{f(\alpha)}$.
"Killing" the maximal antichains in $T | \alpha$ which are in $L_{f(\alpha)}$ relies on the following fact, for which only a proof sketch is given.
If $S$ is a countable family of maximal antichains in $T | \alpha$ then we can construct $U_\alpha$ such that each $A \in S$ in maximal in $T | ( \alpha + 1 )$ (and hence in $T$).
The proof goes as in Lemma 3: for every $x \in T$, one easily finds an $\alpha$-branch through $x$ which meets each $A \in S$; these branches are to be extended.
At this point it is fairly clear what the basic construction of $T$ is, and the question should be answerable without actually opening up the paper. (I also took advantage of MO's citation helper, though I did make some tweaks to its output.)
The question has been formatted into separate paragraphs for easier reading. It has also been organised so that the basic question ("Why is $T$ in $L_{\omega_2}$?") appears very early, at which point it is already clear (to an expert in set-theory) what sort of objects are being discussed. Only later are more specific details given. This allows users to drop out of reading the question early if find they are uninterested in/unknowledgeable of the subject matter.
Yes, asking a question this way takes a lot more time and effort than simply directing users to an external source. It also demands much less effort on the part of potential answerers.
While we're at it, let's talk about titles.
Why does $T$ belong to $L_{\omega_2}$?
would be an absolutely terrible title. It gives no clue whatsoever about the sort of objects that are involved.
A question about Jech's "Trees"
is only marginally better. While it gives the source of the question, it is not really descriptive of the specific question itself.
Why does this Suslin tree belong to $L_{\omega_2}$?
Is, IMHO, a much better option. It gives some sense of the objects that are involved in the question itself. Users reading that title from a general question list should be able to determine whether it is even worth their while to click through.
There are certainly even better options out there to be discovered.
