PP-2020-12:
Bezhanishvili, Guram and Bezhanishvili, Nick
(2020)
*Jankov formulas and axiomatization techniques for intermediate logics.*
[Pre-print]

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## Abstract

We discuss some of Jankov’s contributions to the study of intermediate logics, including the development of what have become known as Jankov formulas and a proof that there are

continuum many intermediate logics. We also discuss how to generalize Jankov’s technique to

develop axiomatization methods for all intermediate logics. These considerations result in what

we term subframe and stable canonical formulas. Subframe canonical formulas are obtained by

working with the disjunction-free reduct of Heyting algebras, and are the algebraic counterpart of

Zakharyaschev’s canonical formulas. On the other hand, stable canonical formulas are obtained by

working with the implication-free reduct of Heyting algebras, and are an alternative to subframe

canonical formulas. We explain how to develop the standard and selective filtration methods algebraically to axiomatize intermediate logics by means of these formulas. Special cases of these

formulas give rise to the classes of subframe and stable intermediate logics, and the algebraic account of filtration techniques can be used to prove that they all posses the finite model property

(fmp). The fmp results about subframe and cofinal subframe logics yield algebraic proofs of the

results of Fine and Zakharyaschev. We conclude by discussing the operations of subframization

and stabilization of intermediate logics that this approach gives rise to.

Item Type: | Pre-print |
---|---|

Report Nr: | PP-2020-12 |

Series Name: | Prepublication (PP) Series |

Year: | 2020 |

Subjects: | Logic Mathematics |

Depositing User: | Nick Bezhanishvili |

Date Deposited: | 25 Jul 2020 18:57 |

Last Modified: | 25 Jul 2020 18:57 |

URI: | https://eprints.illc.uva.nl/id/eprint/1744 |

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