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arXiv 2011.114252020-11math.LO

Are all natural numbers the same

Mirna Džamonja

备注：: A submission for possible publication in the the collection Research Trends in Contemporary Logic (edited by Melvin Fitting, Dov Gabbay, Massoud Pourmahdian, Adrian Rezus, and Ali Sadegh Daghighi) to be published by College Publications in 2020. This version after the 2nd referee report

英文摘要：

This is a report on state-of-the-art on the question of developing higher analogues of the forcing axiom PFA. Recently there have been several attempts to develop forcing axioms analogous to the proper forcing axiom (PFA) for cardinals of the form aleph_n where n > 1. We investigate the difficulties of doing this and survey some of the successes

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