Effective Descriptive Set Theory
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Home > Art, Film & Photography > Effective Descriptive Set Theory: Arithmetical Hierarchy, Analytical Hierarchy, Arithmetical Set, Effective Polish Space, Lightface Analytic Game
Effective Descriptive Set Theory: Arithmetical Hierarchy, Analytical Hierarchy, Arithmetical Set, Effective Polish Space, Lightface Analytic Game

Effective Descriptive Set Theory: Arithmetical Hierarchy, Analytical Hierarchy, Arithmetical Set, Effective Polish Space, Lightface Analytic Game


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About the Book

Chapters: Arithmetical Hierarchy, Analytical Hierarchy, Arithmetical Set, Effective Polish Space, Lightface Analytic Game. Source: Wikipedia. Pages: 30. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The arithmetical hierarchy is important in recursion theory, effective descriptive set theory, and the study of formal theories such as Peano arithmetic. The Tarski-Kuratowski algorithm provides an easy way to get an upper bound on the classifications assigned to a formula and the set it defines. The hyperarithmetical hierarchy and the analytical hierarchy extend the arithmetical hierarchy to classify additional formulas and sets. The arithmetical hierarchy assigns classifications to the formulas in the language of first-order arithmetic. The classifications are denoted and for natural numbers n (including 0). The Greek letters here are lightface symbols, which indicates that the formulas do not contain set parameters. If a formula is logically equivalent to a formula with only bounded quantifiers then is assigned the classifications and . The classifications and are defined inductively for every natural number n using the following rules: In other words, a formula is equivalent to a formula that begins with some existential quantifiers and alternates times between series of existential and universal quantifiers; while a formula is equivalent to a formula that begins with some universal quantifiers and alternates similarly. Because every formula is equivalent to a formula in prenex normal form, every formula with no set quantifiers is assigned at least one classif...More: http: //booksllc.net/?id=18647


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Product Details
  • ISBN-13: 9781158376100
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Arithmetical Hierarchy, Analytical Hierarchy, Arithmetical Set, Effective Polish Space, Lightface Analytic Game
  • Width: 229 mm
  • ISBN-10: 1158376103
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 59 gr


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