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Interpretations of the first-order theory of diagonalizable algebras in Peano arithmetic. (English) Zbl 0463.03015

MSC:
03C05 Equational classes, universal algebra in model theory
08C10 Axiomatic model classes
06E10 Chain conditions, complete algebras
03C60 Model-theoretic algebra
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[1] C. Bernardi,The uniqueness of the fixed points in every diagonalizable algebra (The algebraization of theories which express Theor; VIII),Studia, Logica 35 (1976), pp. 335-343. · Zbl 0345.02020
[2] S. Feferman,Arithmetization of metamathematics in a general setting,Fundamenta Mathematicae 49 (1960), · Zbl 0095.24301
[3] R. Magari,The diagonalizable algebras (The algebraization of theories which express Theor; II),Bolletino della Unione Matematica Italiana (4), 12, Suppl. fasc. 3 (1975), pp. 117-125. · Zbl 0352.08009
[4] ?,Representation and duality theory for diagonalizable algebras (The algebraization of theories which express Theor; IV),Studia Logica 34 (1975), pp. 305-313. · Zbl 0355.02021
[5] ?,On the autological character of diagonalizable algebras (The algebraization of theories which express Theor; VII),Studia Logica 35 (1976), pp. 327-333. · Zbl 0359.02027
[6] G. Sambin,An effective fixed-point theorem in intuitionistic diagonalizable algebras (The algebraization of theories which express Theor; IX),Studia Logica 35 (1976), pp. 345-361. · Zbl 0357.02028
[7] R. Solovay,Provability interpretations of modal logic,Journal of Mathematics 25 (1976), pp. 287-304. · Zbl 0352.02019
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