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The Rowland Institute for Science, 100 Cambridge Parkway, Cambridge, Massachusetts 02142, U.S.A. A construction is presented for generating sentences that satisfy a recursively enumerable set of interpretability properties. This construction is then used to prove three previously announced results concerning the lattice of local interpretability types of theories (also known as the Lattice of Chapters).

Degrees of interpretability

Vítězslav Švejdar (1978)

Commentationes Mathematicae Universitatis Carolinae

Independent instances for some undecidable problems

Cristian Calude, Gheorghe Păun (1983)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Interpretationen der Heyting-Arithmetik endlicher Typen.

Martin Stein (1978)

Archiv für mathematische Logik und Grundlagenforschung

Interpreting reflexive theories in finitely many axioms

V. Shavrukov (1997)

Fundamenta Mathematicae

For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of $\prod_{1}$ (as well as $\sum_{1}$ ) sentences π such that GB interprets ZF+π is $Σ_{3}^{0}$ -complete.

Modal Translations of Heyting and Peano Arithmetic

Kosta Došen (1990)

Publications de l'Institut Mathématique

O druhém Hilbertově problému (Otázka bezespornosti aritmetiky)

Jiří Bečvář (1971)

Pokroky matematiky, fyziky a astronomie

On interpretability in theories containing arithmetic. II.

Petr Hájek (1981)

Commentationes Mathematicae Universitatis Carolinae

Partial conservativity revisited

Petr Hájek (1987)

Commentationes Mathematicae Universitatis Carolinae

Shiftings of the horizon

Antonín Sochor, Petr Vopěnka (1983)

Commentationes Mathematicae Universitatis Carolinae

Some comments on the paper by Artigue, Isambert, Perrin and Zalc

W. Marek (1978)

Fundamenta Mathematicae

Some remarks on bicommutability

M. Artigue, E. Isambert, M. Perrin, A. Zalc (1978)

Fundamenta Mathematicae

Spielquantorinterpretationen unstetiger Funktionale der höheren Analysis.

Wolfgang Friedrich (1984)

Archiv für mathematische Logik und Grundlagenforschung

Sul problema dell'autoriferimento

Ennio De Giorgi, Marco Forti, Vincenzo M. Tortorelli (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We formulate, within the frame-theory $Q$ for the foundations of Mathematics outlined in [2], a list $L$ of axioms which state that almost all "interesting" collections and almost all "interesting" operations are elements of the universe. The resulting theory $Q+L$ would thus have the important foundational feature of being completely self-contained. Unfortunately, the whole list $L$ is inconsistent, and we are led to formulate the following problem, which we call the problem of self-reference: "Find out...

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