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Article Dans Une Revue The Journal of Symbolic Logic Année : 1996

Stretchings

Olivier Finkel
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  • PersonId : 834645
Jean-Pierre Ressayre
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  • PersonId : 835640

Résumé

A structure is locally finite if every finitely generated substructure is finite; local sentences are universal sentences all models of which are locally finite. The stretching theorem for local sentences expresses a remarkable reflection phenomenon between the finite and the infinite models of local sentences. This result in part requires strong axioms to be proved; it was studied by the second named author [J.S.L. 53, No. 4, p. 1009-1026]. Here we correct and extend this paper; in particular we show that the stretching theorem implies the existence of inaccessible cardinals, and has precisely the consistency strength of Mahlo cardinals of finite order. And we present a sequel due to the first named author: (i) decidability of the spectrum Sp( phi ) of a local sentence phi, below omega^omega ; where Sp( phi ) is the set of ordinals alpha such that phi has a model of order type alpha; (ii) proof that beth_omega =sup { Sp( phi ) : phi local sentence with a bounded spectrum}; (iii) existence of a local sentence phi such that Sp( phi ) contains all infinite ordinals except the inaccessible cardinals.
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Dates et versions

hal-00103669 , version 1 (05-10-2006)

Identifiants

  • HAL Id : hal-00103669 , version 1

Citer

Olivier Finkel, Jean-Pierre Ressayre. Stretchings. The Journal of Symbolic Logic, 1996, 61 (2), pp.563-585. ⟨hal-00103669⟩
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