Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical System of Martin-Lof's Inductive Definitions is not Equivalent
  to Cyclic Proofs   A cyclic proof system, called CLKID-omega, gives us another way of
representing inductive definitions and efficient proof search. The 2005 paper
by Brotherston showed that the provability of CLKID-omega includes the
provability of LKID, first order classical logic with inductive definitions in
Martin-L\"of's style, and conjectured the equivalence. The equivalence has been
left an open question since 2011. This paper shows that CLKID-omega and LKID
are indeed not equivalent. This paper considers a statement called 2-Hydra in
these two systems with the first-order language formed by 0, the successor, the
natural number predicate, and a binary predicate symbol used to express
2-Hydra. This paper shows that the 2-Hydra statement is provable in
CLKID-omega, but the statement is not provable in LKID, by constructing some
Henkin model where the statement is false.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics