Consequences of Arithmetic for Set Theory

@article{Halbeisen1994ConsequencesOA,
  title={Consequences of Arithmetic for Set Theory},
  author={L. Halbeisen and S. Shelah},
  journal={J. Symb. Log.},
  year={1994},
  volume={59},
  pages={30-40}
}
In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D; either CD or DC: However, in ZF this is no longer so. For a given inflnite set A consider seq 1 1 (A), the set of all sequences of A without repetition. We compare seq 1 1 (A) , the cardinality of this set, to P(A) , the cardinality of the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that… Expand
19 Citations
FACTORIALS OF INFINITE CARDINALS IN ZF PART II: CONSISTENCY RESULTS
Cardinal Relations in ZF Only
Relations Between Some Cardinals in the Absence of the Axiom of Choice
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Models of Set Theory with Atoms
A Note on Weakly Dedekind Finite Sets
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A weird relation between two cardinals
  • L. Halbeisen
  • Mathematics, Computer Science
  • Arch. Math. Log.
  • 2018
  • 2
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FACTORIALS OF INFINITE CARDINALS IN ZF PART I: ZF RESULTS
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