"The real line in elementary submodels of set theory" appeared in The Journal of Symbolic Logic 65 (2000), no. 2, 683–691. doi.org/10.2307/2586561

This fun paper was written by Ken and Frank Tall. It appeared while I was in grad school.

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I only interacted with him very briefly, but his good humor was always apparent.

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Kunen was the first to prove this.

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"Saturated ideals", J. Symbolic Logic 43 (1978), no. 1, 65–76. doi.org/10.2307/2271949

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Oh, well. 🙂

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mathoverflow.net/q/40507/6085

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elsevier.com/books/set-theo…

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Kunen, K.; Paris, J. B. "Boolean extensions and measurable cardinals". Ann. Math. Logic 2 (1970/71), no. 4, 359–377.

doi.org/10.1016/0003-4…

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The combinatorics of Reinhardt cardinals (the critical points of embeddings j:V→V in the absence of choice) are really interesting.

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I've also looked at extensions of the inconsistency result in my own work. I became interested in this after obtaining some results relating the structure of V and an inner model W, from the assumption that V and W agree on some cardinals.

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andrescaicedo.files.wordpress.com/2010/04/cardin…

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Any embedding j:V→M with M and V having the same cardinals must be highly discontinuous, that is,

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Very recently, Gabe Goldberg extended this idea, by showing that,

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