Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A non-compact deduction rule for the logic of provability and its
  algebraic models   In this paper, we introduce a proof system with a non-compact deduction rule,
that is, a deduction rule with countably many premises, to axiomatize the logic
$\mathbf{GL}$ of provability, and show its Kripke completeness in an algebraic
manner. As $\mathbf{GL}$ is not canonical, a standard proof of Kripke
completeness for $\mathbf{GL}$ is given by a Kripke model which is obtained by
changing the binary relation of the canonical model, while our proof is given
by a submodel of the canonical model of $\mathbf{GL}$ which is obtained by
making use of an infinitary extension of the J\'{o}nsson-Tarski representation.
We also show the three classes of algebras defined by $\Box x\leq\Box\Box x$
and one of the following three conditions,
$\bigwedge_{n\in\omega}\Diamond^{n}1=0$, the non-compact deduction rule and the
L\"{o}b formula, are mutually different, while all of them define
$\mathbf{GL}$.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin