Extendible Formulas in Two Variables in Intuitionistic Logic

Bezhanishvili, Nick; Jongh, Dick de

doi:10.1007/s11225-012-9389-8

Cited by 7 publications

(4 citation statements)

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“…When the set of variables under consideration is at most one, then there are but finitely many exact models up to isomorphism. The situation changes drastically from two variables onwards, as in this situation there are infinitely many non-isomorphic exact models, as shown by Bezhanishvili and de Jongh (2012). To get around this problem, we switch to a different notion of model in Section 4.…”

Section: Lemma (Ghilardi 1999 Proposition 2)mentioning

confidence: 99%

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Decidability of Admissibility: On a Problem by Friedman and Its Solution by Rybakov

Goudsmit¹

2020

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Rybakov (1984a) proved that the admissible rules of IPC are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility. * Support by the Netherlands Organisation for Scientific Research under grant 639.032.918 is gratefully acknowledged.

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Section: Lemma (Ghilardi 1999 Proposition 2)mentioning

confidence: 99%

“…This, in turn, entails the extendibility of U via Lemma 3.8 orBezhanishvili and de Jongh (2012, Theorem 4.17). For more details on this correspondence, we refer to the latterBezhanishvili and de Jongh (2012) in the general case and toArevadze (2001) in the case where U is finite.…”

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confidence: 99%

Decidability of Admissibility: On a Problem by Friedman and Its Solution by Rybakov

Goudsmit¹

2020

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“…Note that all endpoints U(n) which are not in X are in B(X). The concept of border point was developed in studied in [2]. Proof.…”

Section: Lemma 47mentioning

confidence: 99%

Jankov’s Theorems for Intermediate Logics in the Setting of Universal Models

Jongh

Yang

2011

Logic, Language, and Computation

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In this article we prove the Jankov Theorem for extensions of IPC ([6]) and the Jankov Theorem for KC ([7]) in a uniform frame-theoretic way in the setting of nuniversal models for IPC. In frame-theoretic terms, the first Jankov Theorem states that for each finite rooted frame there is a formula ψ with the property that any counter-model for ψ needs this frame in the sense that each descriptive frame that falsifies ψ will have this frame as the p-morphic image of a generated subframe. The second one states that KC is the strongest logic that proves no negationless formulas beyond IPC. On the way we give a simple proof of the fact discussed and proved in [1] that the upper part of the n-Henkin model H(n) is isomorphic to the n-universal model U(n) of IPC. All these results earlier occurred in a somewhat different form in [8].

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“…The uniform interpolation property can be used as a tool in the study of admissible rules. It is used by de Jongh and Visser (1996) to characterize so-called exact formulas in IPC that in this logic correspond to projective formulas (see also, de Jongh and Chagrova, 1995;Bezhanishvili and de Jongh, 2012). Goudsmit (2015) observes the same for the seven consistent intermediate logics that have uniform interpolation (Ghilardi and Zawadowski, 1997).…”

Section: General Future Directionsmentioning

confidence: 99%

Uniform Interpolation and Admissible Rules

Giessen¹

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Ik bedank de wiskundemeiden Anita, Daja, Heleen, Jo-anne en Simone. Wat een geweldige studietijd heb ik met jullie beleefd. Ik hoop dat mijn proefschrift weer een vlaag van herkenning en vreugde bij jullie oproept bij het lezen van 'Definition' dit en 'Theorem' dat. Simone, Lotte en Eline, bedankt voor het doorploegen van de Nederlandse samenvatting. Ik bedank al mijn vrienden voor alle gezelligheid.Papa en mama, wat fijn dat jullie altijd achter me staan. Ik moest mezelf vaak herinneren aan mijn moeders wijsheid: 80% is goed genoeg! Papa, bedankt voor al je grapjes over π (deze is de enige die je in dit proefschrift zult vinden). David en Judith, jullie zijn mijn geweldige broer en zus. David, het is leuk dat we beide een achtergrond hebben in de wiskunde en dat je net zo gek bent als ik om Carcassonne te spelen met alle uitbreidingen. Judith, ik bewonder je lef en volg je voetsporen om na mijn PhD verder onderzoek te doen in het buitenland. Wij zijn nog lang niet uitgegiecheld :) Esther en Winfried, wat fijn om jullie als schoonouders te hebben en ik ben blij dat de deur altijd bij jullie open staat. Valijn, je brengt me aan het lachen, je troost me, je begrijpt me, je laat me en je maakt me gelukkig.

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Extendible Formulas in Two Variables in Intuitionistic Logic

Cited by 7 publications

References 16 publications

Decidability of Admissibility: On a Problem by Friedman and Its Solution by Rybakov

Decidability of Admissibility: On a Problem by Friedman and Its Solution by Rybakov

Jankov’s Theorems for Intermediate Logics in the Setting of Universal Models

Uniform Interpolation and Admissible Rules

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