Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categoricity and infinitary logics   We point out a gap in Shelah's proof of the following result:
  $\mathbf{Claim}$
  Let $K$ be an abstract elementary class categorical in unboundedly many
cardinals. Then there exists a cardinal $\lambda$ such that whenever $M, N \in
K$ have size at least $\lambda$, $M \le N$ if and only if $M
\preceq_{L_{\infty, \text{LS} (K)^+}} N$.
  The importance of the claim lies in the following theorem, implicit in
Shelah's work:
  $\mathbf{Theorem}$
  Assume the claim. Let $K$ be an abstract elementary class categorical in
unboundedly many cardinals. Then the class of $\lambda$ such that:
  1) $K$ is categorical in $\lambda$;
  2) $K$ has amalgamation in $\lambda$; and
  3) there is a good $\lambda$-frame with underlying class $K_\lambda$
  is stationary.
  We give a proof and discuss some related questions.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci