Isomorphic limit ultrapowers for infinitary logic

2018/10/29 by Shelah, Saharon
#03C30 #03C45 #03C55 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1810.12729

Abstract

The logic L¹_θintroduced in [Sh:797]; it is the maximal logic below L_theta theta in which a well ordering is not definable. We investigate it for theta a compact cardinal. We prove it satisfies several parallel of classical theorems on first order logic, strengthening the thesis that it is a natural logic. In particular, two models are L¹_theta-equivalent iff for some omega-sequence of theta-complete ultrafilters, the iterated ultra-powers by it of those two models are isomorphic.

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