• Corpus ID: 201650641

A universal characterization of standard Borel spaces

  title={A universal characterization of standard Borel spaces},
  author={Ruiyuan Chen},
  journal={arXiv: Logic},
We prove that the category $\mathsf{SBor}$ of standard Borel spaces is the (bi-)initial object in the 2-category of countably complete Boolean (countably) extensive categories. This means that $\mathsf{SBor}$ is the universal category admitting some familiar algebraic operations of countable arity (e.g., countable products, unions) obeying some simple compatibility conditions (e.g., products distribute over disjoint unions). More generally, for any infinite regular cardinal $\kappa$, the dual… 

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  • V. Selivanov
  • Mathematics
    Mathematical Structures in Computer Science
  • 2016
The paper tries to extend some results of the classical Descriptive Set Theory to as many countably based T 0-spaces (cb0-sp spaces) as possible and investigates the difference hierarchy of k-partitions and the fine hierarchy closely related to the Wadge hierarchy.

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I. Categories, Functors and Natural Transformations.- 1. Axioms for Categories.- 2. Categories.- 3. Functors.- 4. Natural Transformations.- 5. Monics, Epis, and Zeros.- 6. Foundations.- 7. Large

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Grothendieck topoi.- Interpretation of the logic in categories.- Axioms and rules of inference valid in categories.- Boolean and heyting valued models.- Completeness.- Existence theorems on geometric