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Construction of sentences with specific interpretability properties

A. Stern (1993)

Fundamenta Mathematicae

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).

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 1 (as well as 1 ) sentences π such that GB interprets ZF+π is Σ 3 0 -complete.

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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