Abstract
We produce a model of \(\mathsf {ZFA}+ \mathsf {PAC}\) such that no outer model of \(\mathsf {ZFAC}\) has the same pure sets, answering a question asked privately by Eric Hall.
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The research of the first author was partially supported by NSF Grant DMS-1201494. The research of the second author was partially supported by the United States-Israel Binational Science Foundation (Grant Number 2010405) and the National Science Foundation (Grant Number 136974). Publication Number 1105 in the second author’s list. We thank the referee for a close reading of the paper and several helpful comments.
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Larson, P., Shelah, S. A model of \(\mathsf {ZFA}+ \mathsf {PAC}\) with no outer model of \(\mathsf {ZFAC}\) with the same pure part. Arch. Math. Logic 57, 853–859 (2018). https://doi.org/10.1007/s00153-018-0610-y
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DOI: https://doi.org/10.1007/s00153-018-0610-y