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MLQ
2007

Local sentences and Mahlo cardinals

13 years 11 months ago
Local sentences and Mahlo cardinals
Local sentences were introduced by Ressayre in [Res88] 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 [FR96]. Here, we solve this problem, using a combinatorial result of J. H. Schmerl [Sch74]. 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 φn which has well ordered models of order type τ, for every infinite ordinal τ > ω which is not an n-Mahlo cardinal. ∗ UMR 5668 - CNRS - ENS Lyon - UCB Lyon - INRIA 1
Olivier Finkel, Stevo Todorcevic
Added 27 Dec 2010
Updated 27 Dec 2010
Type Journal
Year 2007
Where MLQ
Authors Olivier Finkel, Stevo Todorcevic
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