Classical Descriptive Set Theory

Kechris, A. S. (1995). Classical Descriptive Set Theory. Springer-Verlag.

Type

Book

Intellectual base

Review or monograph

Year

1995

DOI

10.1007/978-1-4612-4190-4

ISBN

9781461286929

Link

https://doi.org/10.1007/978-1-4612-4190-4

Cited by

7 citations across 7 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Borel Set
  • Thus Borel sets are exactly those obtainable from open sets by iterating complement and countable union (and hence countable intersection).
• Effective Polish space
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Gδ Set
  • Gδ sets are one of the first nontrivial classes in the Borel hierarchy and are commonly written Π⁰₂ in modern descriptive-set-theoretic notation

    This sourceKechris's treatment of the Borel hierarchy fixes the boldface numbering in which the G-delta sets are exactly the Pi^0_2 sets, the second multiplicative class.

• Kleene–Brouwer Order
  • This correspondence turns tree well-foundedness into order well-foundedness and is used in computability, descriptive set theory, proof theory, and ordinal analysis.
• Set-Theoretic Code
  • This coding move lets descriptive set theory study hereditarily countable objects inside standard spaces of reals.
• Standard Borel space
  • … identity and a convenient observable transfers from Any uncountable Polish space with its Borel sigma-algebra is Borel-isomorphic to every other uncountable standard Borel space. to A probability model checks standard-Borel hypotheses before invoking regular conditional distributions or measurable selection results..
• Universally measurable set
  • Equivalent probability-measure formulations use normalization, while universal measurability is weaker than being Borel and stronger than measurability for one selected measure; set-theoretic axioms affect broad projective classes.

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