Corpus ID: 115178762

Forcing Differentiable Functions

@article{Kunen2009ForcingDF,
  title={Forcing Differentiable Functions},
  author={K. Kunen},
  journal={arXiv: Logic},
  year={2009}
}
  • K. Kunen
  • Published 2009
  • Mathematics
  • arXiv: Logic
In various models of set theory, we consider covering Aleph_1 x Aleph_1 rectangles by countably many smooth curves, and we study differentiable isomorphisms between Aleph_1-dense sets of reals. 
1 Citations
Homeomorphisms with Small Twist
We extend Baumgartner's result on isomorphisms of aleph_1 dense subsets of the reals R in two ways: First, the function can be made to be absolutely continuous. Second, one can replace R by R^n.

References

SHOWING 1-7 OF 7 REFERENCES
Arcs in the plane
Abstract Assuming PFA, every uncountable subset E of the plane meets some C 1 arc in an uncountable set. This is not provable from MA ( ℵ 1 ) , although in the case that E is analytic, this is a ZFCExpand
Everywhere differentiable, nowhere monotone functions
In this thesis we give a Baire Category type proof of the existence of functions F : R -* R which are differentiable at every point but monotone on no interval having positive length and whoseExpand
Martin’s axiom does not imply that every two ℕ1-dense sets of reals are isomorphic
Assuming the consistency of ZFC we prove the claim in the title by showing the consistency with ZFC of: There exists a set of realsA such that every function fromA toA is order preserving on anExpand
On the consistency of some partition theorems for continuous colorings, and the structure of aleph1-dense real order types
TLDR
It is proved that for every finite model : Con(MA+ ≏ ) iff L is a distributive lattice, and it is consistent that the Magidor-Malitz language is not countably compact. Expand
Applications of the Proper Forcing Axiom
Publisher Summary The chapter presents a more powerful version of Martin Axiom (MA), the Proper Forcing Axiom (PFA) that is successful at settling problems left open by MA. PFA is obtained from MA byExpand