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Hopfian groups have been a topic of interest in alge-braic settings for many years. In this work a natural generalizationof the notion, so-called R-Hopficity is introduced. Basic propertiesof R-Hopfian groups are developed and the question of whether ornot infinite direct products of copies of the integers are R-Hopfian isconsidered. An unexpected result is that the answer to this purelyalgebraic question depends on the set theory assumed.
Goldsmith, B. (2018) Generalised Hopficity and Products of the Integers, Irish Math. Soc. Bulletin, Number 80, Winter 2017, 21–33, ISSN 0791-5578.