2 citations · 4 across the 8 of their papers we have counts for
8 papers
An Easton-like Theorem for Zermelo-Fraenkel Set Theory with the Axiom of Dependent Choice
Anne Fernengel, Peter Koepke
We show that in the theory ZF + DC + for every cardinal λ, the set of infinite subsets of λ is well-ordered (i.e., Shelah's AX4), the θ-function measuring the surjective size of th…
An Easton-like theorem for Zermelo-Fraenkel Set Theory without Choice
Anne Fernengel, Peter Koepke
We show that in Zermelo-Fraenkel Set Theory without the Axiom of Choice a surjectively modified continuum function can take almost arbitrary values for all infinite cardinal…
An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report)
Anne Fernengel, Peter Koepke
By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In…
Violating the Singular Cardinals Hypothesis Without Large Cardinals
Moti Gitik, Peter Koepke
We extend a transitive model V of ZFC + GCH cardinal preservingly to a model N of ZF + "GCH holds below Alef_omega" + "there is a surjection from the power set of Alef_omega onto l…
Global Square and Mutual Stationarity at the Aleph_n
Peter Koepke, Philip Welch
We show using a proof of the Global Square property in Core Models below a measurable of Mitchell order o(kappa)=kappa^++ (a result originally due to Jensen & Zeman) that Foreman a…
The Theory of Sets of Ordinals
Peter Koepke, Martin Koerwien
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO…