Local Sentences and Mahlo Cardinals

Abstract : Local sentences were introduced by J.-P. Ressayre who proved certain remarkable stretching theorems establishing the equivalence between the existence of finite models for these sentences and the existence of some infinite well ordered models. Two of these stretching theorems were only proved under certain large cardinal axioms but the question of their exact (consistency) strength was left open in [O. Finkel and J.-P. Ressayre, Stretchings, Journal of Symbolic Logic, Volume 61 ( 2), 1996, p. 563-585 ]. Here, we solve this problem, using a combinatorial result of J. H. Schmerl. In fact, we show that the stretching principles are equivalent to the existence of n-Mahlo cardinals for appropriate integers n. This is done by proving first that for each integer n, there is a local sentence phi_n which has well ordered models of order type alpha, for every infinite ordinal alpha > omega which is not an n-Mahlo cardinal.
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Contributeur : Olivier Finkel <>
Soumis le : mercredi 16 mai 2007 - 10:25:29
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
Document(s) archivé(s) le : mercredi 7 avril 2010 - 02:20:50


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  • HAL Id : hal-00147192, version 1
  • ARXIV : 0705.2298



Olivier Finkel, Stevo Todorcevic. Local Sentences and Mahlo Cardinals. Mathematical Logic Quaterly, 2007, 53 (6), pp.558-563. ⟨hal-00147192⟩



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