Splitting stationary sets from weak forms of Choice

@article{Larson2009SplittingSS,
  title={Splitting stationary sets from weak forms of Choice},
  author={Paul B. Larson and Saharon Shelah},
  journal={Mathematical Logic Quarterly},
  year={2009},
  volume={55}
}
  • P. Larson, S. Shelah
  • Published 1 June 2009
  • Chemistry, Mathematics
  • Mathematical Logic Quarterly
Working in the context of restricted forms of the Axiom of Choice, we consider the problem of splitting the ordinals below λ of cofinality θ into λ many stationary sets, where θ < λ are regular cardinals. This is a continuation of [4] (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 
8 Citations
Pcf without Choice Sh835
We mainly investigate models of set theory with restricted choice, e.g., ZF + DC + the family of countable subsets of λ is well ordered for every λ (really local version for a given λ). We think that
PCF arithmetic without and with choice
We deal with relatives of GCH which are provable. In particular, we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice
PCF ARITHMETIC WITHOUT AND WITH CHOICE SH938
We deal with relatives of GCH which are provable. In particular we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice
ZF + DC + AX4
TLDR
It is proved that for a sequence δ¯=⟨δs: s∈Y⟩,cf(δ s) large enough compared to Y, the pcf theorem can be proved with minor changes (in particular, using true cofinalities not the pseudo ones).
LIST OF PUBLICATIONS
1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New
LIST OF PUBLICATIONS
1. Sh:a Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam-New
Partitioning a reflecting stationary set
We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to
ZF+DC+AX_4
We consider mainly the following version of set theory: "ZF + DC and for every lambda, lambda^{aleph_0} is well ordered", our thesis is that this is a reasonable set theory, e.g. on the one hand it

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