Title: Theory / Unimportant / Math / Logic / recursion theory / Odifreddi / 0 Introduction;

Name: Classical Recursion Theory
Definition: Study of the real numbers
Page: 1
Chapter: Introduction
Context: Some logic
Definition2: Study of the function over the natural numbers
Conjdef: Either

Name: A hierarchy
Definition: A stratification of a class of reals built from below, starting from a subclass that is taken as primitive (either because well understood, or because already previously analyzed), and obtained by iteration of a n operation of class construction.
Page: 2
Chapter: Introduction
Section: What is in the book

Name: A degree
Definition: An equivalence classes of reals under given equivalence relations, that identify reals with similar properties.
Page: 2
Chapter: Introduction
Section: What is in the book
Context: Recursion theory

Name: The disjoint union of \(A\) and \(B\)
Definition: \(2A+(2B+1)\)
Page: 14
Chapter: Introduction
Section: Notations and conventions
Variables: \(A,B\subseteq\mathbb N\)
Context: Sets of naturals
Notation: \(A\oplus B\)

Name: The recursive product of \(A\) and \(B\)
Definition: The set of codes \(\langle x,y\rangle\) for \((x,y)\in A\times B\)
Page: 14
Chapter: Introduction
Section: Notations and conventions
Variables: \(A,B\subseteq\mathbb N\)
Context: Recursion theory
Notation: \(A\cdot B\)
Typ: A subset of \(\mathbb N\)

Name: The characteristic function of \(A\)
Definition: The function sending elements of \(A\) to 1 and everything else to 0
Page: 14
Chapter: Introduction
Section: Notations and conventions
Variables: \(A\subseteq B\)
Context: Recursion theory
Notation: \(c_A\)

Definition: \(\phi\) is defined on \(x\)
Page: 16
Chapter: Introduction
Section: Notations and conventions
Variables: \(\phi\) a function,
\(x\) an element
Notation: \(\phi(x)\downarrow\)

Definition: \(\phi\) is undefined on \(x\)
Page: 16
Chapter: Introduction
Section: Notations and conventions
Variables: \(\phi\) a function,
\(x\) an element
Notation: \(\phi(x)\uparrow\)

Definition: \(\phi\) and \(\psi\) are equal as partial functions.
Page: 16
Chapter: Introduction
Section: Notations and conventions
Variables: \(\phi,\psi\) partial functions
Notation: \(\phi\simeq\psi\)

Name: The graph of \(\phi\)
Definition: The set of pairs \((x,\phi(x))\)
Page: 16
Chapter: Introduction
Section: Notations and conventions
Variables: \(\phi\) functions

Definition: \(\beta\) extends \(\alpha\) as partial functions
Page: 16
Chapter: Introduction
Section: Notations and conventions
Variables: \(\alpha,\beta\) functions
Notation: \(\alpha\subseteq\beta\)