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arXiv · 1810.12729

Isomorphic limit ultrapowers for infinitary logic

Saharon Shelah
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Abstract

The logic L^1_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 L^1_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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Saharon Shelah. 2021-08-09. Isomorphic limit ultrapowers for infinitary logic. https://arxiv.org/abs/1810.12729

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