### Abstract

We describe the n-universal model U^{⋆}(n) of the positive fragment of the intuitionistic propositional calculus IPC. We show that U^{⋆}(n) is isomorphic to a generated submodel of U(n) - the n-universal model of IPC. Using U^{⋆}(n), we give an alternative proof of Jankov’s theorem stating that the intermediate logic KC, the logic of the weak law of excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same positive formulas as IPC.

Original language | English |
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Title of host publication | Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers |

Editors | Mehrnoosh Sadrzadeh, Henk Zeevat, Sarah E. Murray, Helle Hvid Hansen |

Publisher | Springer Verlag |

Pages | 229-250 |

Number of pages | 22 |

ISBN (Print) | 9783662543313 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

Externally published | Yes |

Event | 11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015 - Tbilisi, Georgia Duration: 21 Sep 2015 → 26 Sep 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10148 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015 |
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Country | Georgia |

City | Tbilisi |

Period | 21/09/15 → 26/09/15 |

### Fingerprint

### Keywords

- Fragment of intuitionistic logic
- Jankov’s theorem
- Positive morphism
- Universal models

### Cite this

*Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers*(pp. 229-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10148 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-54332-0_13

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*Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10148 LNCS, Springer Verlag, pp. 229-250, 11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015, Tbilisi, Georgia, 21/09/15. https://doi.org/10.1007/978-3-662-54332-0_13

**Universal models for the positive fragment of intuitionistic logic.** / Bezhanishvili, Nick; de Jongh, Dick; Tzimoulis, Apostolos; Zhao, Zhiguang.

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Universal models for the positive fragment of intuitionistic logic

AU - Bezhanishvili, Nick

AU - de Jongh, Dick

AU - Tzimoulis, Apostolos

AU - Zhao, Zhiguang

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We describe the n-universal model U⋆(n) of the positive fragment of the intuitionistic propositional calculus IPC. We show that U⋆(n) is isomorphic to a generated submodel of U(n) - the n-universal model of IPC. Using U⋆(n), we give an alternative proof of Jankov’s theorem stating that the intermediate logic KC, the logic of the weak law of excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same positive formulas as IPC.

AB - We describe the n-universal model U⋆(n) of the positive fragment of the intuitionistic propositional calculus IPC. We show that U⋆(n) is isomorphic to a generated submodel of U(n) - the n-universal model of IPC. Using U⋆(n), we give an alternative proof of Jankov’s theorem stating that the intermediate logic KC, the logic of the weak law of excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same positive formulas as IPC.

KW - Fragment of intuitionistic logic

KW - Jankov’s theorem

KW - Positive morphism

KW - Universal models

UR - http://www.scopus.com/inward/record.url?scp=85014221857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014221857&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-54332-0_13

DO - 10.1007/978-3-662-54332-0_13

M3 - Conference contribution

SN - 9783662543313

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 229

EP - 250

BT - Logic, Language, and Computation - 11th International Tbilisi Symposium, TbiLLC 2015, Revised Selected Papers

A2 - Sadrzadeh, Mehrnoosh

A2 - Zeevat, Henk

A2 - Murray, Sarah E.

A2 - Hansen, Helle Hvid

PB - Springer Verlag

ER -