The Morris model

@article{Karagila2018TheMM,
  title={The Morris model},
  author={Asaf Karagila},
  journal={arXiv: Logic},
  year={2018}
}
Douglass B. Morris announced in 1970 that it is consistent with ZF that "For every $\alpha$, there exists a set $A_\alpha$ which is the countable union of countable sets, and $\mathcal P(A_\alpha)$ can be partitioned into $\aleph_\alpha$ non-empty sets". The result was never published in a journal, and seems to have been lost, save a mention in Jech's "Axiom of Choice". We provide a proof using modern tools derived from recent work of the author. We also prove a new preservation theorem for… Expand
2 Citations
Iterated failures of choice
Preserving Dependent Choice

References

SHOWING 1-10 OF 10 REFERENCES
The Bristol model: An abyss called a Cohen real
The Axiom of Choice
ITERATING SYMMETRIC EXTENSIONS
  • Asaf Karagila
  • Mathematics, Computer Science
  • The Journal of Symbolic Logic
  • 2019
Fodor’s lemma can fail everywhere
All uncountable cardinals can be singular
Preserving Dependent Choice
L O ] 1 J ul 2 01 6 An Easton-like theorem for Zermelo-Fraenkel Set Theory without Choice
  • 2018
An Easton-like theorem for Zermelo–Fraenkel set theory without choice, ArXiv e-prints
  • 2016
The axiom of choice, North-Holland Publishing Co., Amsterdam-London; Amercan Elsevier Publishing Co., Inc
  • New York,
  • 1973
Adding total indiscernibles to models of set theory
  • Ph.D. thesis,
  • 1970