Publications

Authors:

Fellin, Giulio; Schuster, Peter

Title:

CONSERVATION AS TRANSLATION

Year:

2025

Type of item:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Language:

Inglese

Format:

A Stampa

Referee:

Sì

Name of journal:

THE REVIEW OF SYMBOLIC LOGIC

ISSN of journal:

1755-0203

N° Volume:

18

Number or Folder:

1

Page numbers:

316-348

Keyword:

Glivenko; nucleus; entailment relation; negative translation; double negation

Short description of contents:

Glivenko's theorem says that classical provability of a propositional formula entails intuitionistic provability of the double negation of that formula. This stood right at the beginning of the success story of negative translations, indeed mainly designed for converting classically derivable formulae into intuitionistically derivable ones. We now generalise this approach: simultaneously from double negation to an arbitrary nucleus; from provability in a calculus to an inductively generated abstract consequence relation; and from propositional logic to any set of objects whatsoever. In particular, we give sharp criteria for the generalisation of classical logic to be a conservative extension of the one of intuitionistic logic with double negation.

Web page:

https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/conservation-as-translation/7D791F8060241B20D370F1030A4030EA

Product ID:

145474

Handle IRIS:

11562/1161331

Last Modified:

May 7, 2025

Bibliographic citation:

Fellin, Giulio; Schuster, Peter, CONSERVATION AS TRANSLATION «THE REVIEW OF SYMBOLIC LOGIC» , vol. 18 , n. 1 , 2025 , pp. 316-348

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