Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internal sizes in $\mu$-abstract elementary classes   Working in the context of $\mu$-abstract elementary classes ($\mu$-AECs) -
or, equivalently, accessible categories with all morphisms monomorphisms - we
examine the two natural notions of size that occur, namely cardinality of
underlying sets and internal size. The latter, purely category-theoretic,
notion generalizes e.g. density character in complete metric spaces and
cardinality of orthogonal bases in Hilbert spaces. We consider the relationship
between these notions under mild set-theoretic hypotheses, including weakenings
of the singular cardinal hypothesis. We also establish preliminary results on
the existence and categoricity spectra of $\mu$-AECs, including specific
examples showing dramatic failures of the eventual categoricity conjecture
(with categoricity defined using cardinality) in $\mu$-AECs.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc