Über das Problem der Wohlordnung

  title={{\"U}ber das Problem der Wohlordnung},
  author={F. Hartogs},
  journal={Mathematische Annalen},
Intuitionistic Sets and Ordinals
  • P. Taylor
  • Computer Science, Mathematics
  • J. Symb. Log.
  • 1996
It is shown how to make the successor monotone by introducing plumpness , which strengthens transitivity, and clarifies the traditional development of successors and unions, making it intuitionistic ; even the (classical) proof of trichotomy is made simpler. Expand
Graph colorings and the axiom of choice
Dv.FINITION 2. Let G ~ (V, E) be a graph. A set S c V is dependent if S contains two adjacent vertices; otherwise it is independent. A function f: V ~ C is a good coloring if f l (c) is independentExpand
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperationExpand
The generalised continuum hypothesis implies the axiom of choice in Coq
Two Coq mechanisations of Sierpinski's result that the generalised continuum hypothesis (GCH) implies the axiom of choice (AC) are discussed and compared, concerning type-theoretic formulations of GCH and AC. Expand
A formal proof of the independence of the continuum hypothesis
We describe a formal proof of the independence of the continuum hypothesis (CH) in the Lean theorem prover. We use Boolean-valued models to give forcing arguments for both directions, using CohenExpand
A Generalization of the Trichotomy Principle
We write X ≼ Y if there is an injection from a set X into a set Y and write X ≼ Y if X = ∅ or there is a surjection from Y onto X. For any sets X and Y , X ≼ Y implies X ≼ Y but the converse cannotExpand
Sets, Models and Proofs
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory, and explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. Expand
Size-based termination of higher-order rewriting
  • F. Blanqui
  • Computer Science, Mathematics
  • Journal of Functional Programming
  • 2018
A general and modular criterion for the termination of simply typed λ-calculus extended with function symbols defined by user-defined rewrite rules is provided. Expand
Axioms of Set Theory
We shall introduce and discuss in this chapter the axioms of Zermelo–Fraenkel Set Theory with the Axiom of Choice.