Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Type Two Cuts, Bad Cuts and Very Bad Cuts   Type two cuts, bad cuts and very bad cuts are introduced by Keisler and Leth
for studying the relationship between Loeb measure and U-topology of a
hyperfinite time line in an $\omega_1$-saturated nonstandard universe. The
questions concerning the existence of those cuts are asked there. In this paper
we answer, fully or partially, some of those questions by showing that: (1)
type two cuts exist in any nonstandard model of Peano Arithmetic, (2) the
$\aleph_1$-isomorphism property implies that bad cuts exist, but no bad cuts
are very bad.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con