# Index – Recursion Theory

## Index

(x)n 1

+o 1

<o 1

<ox 1

C(σ) 1

DefA(X) 1

Gf 1

Hn 1

J[A] 1

K-triviality 1

K(σ) 1

L[A] 1

WO1 1

[T] 1

[σ] 1

RA(U) 1

SA(U) 1

Γ 1

* 1

x 1

MA 1

MAκ 1

Ω 1

-inductive principle 1

-random cuppable 1

Σn-Skolem function 1

Σn(M) 1

Σβ(HYP) 1

Σγ 1

1

WF0 1

WF1 1

WO0 1

Σ 1

κ-closed 1

〈.〉 1

C 1

K 1

M 1

T 1

(, x) 1

(α, x) 1

HF 1

rk 1

(, ) 1

(α, ) 1

BC 1

BC(HYP) 1

DNR 1

h- 1

Low(Γ) 1

1

M 1

φ1

φ(x | ψ) 1

|| 1

||x 1

|σ| 1

a-generic 1

g > f 1

i*(τ) 1

o(M) 1

x1

xσ 1

xn 1

x+ 1

x[n] 1

OD(A)M 1

HOD(A)M 1

HODM 1

Ret(γ, p, q) 1

val(τ, G) 1

KP 1

ODM 1

<o* 1

M 1

Absolute 1

–downward 1

–upward 1

Almost disjoint set 1

Antichain 1

– antichain of conditions 1

Axiom

-comprehension- 1

– Martin’s 1

Axiom of determinacy 1

Base

– for a cone of Γ-randomness 1

Base for P 1

Base for randomness 1

Canonical Σ1-Skolem function 1

Cardinal

– inaccessible 1

– measurable 1

– weakly inaccessible 1

Chain 1

– cofinal 1

Chain condition

κ- 1

Code

– hyperarithmetic 1

–Borel 1

Condition 1

Definable

-uniformly 1

Definable 1

Dense embedding 1

Domination

– recursive 1

Elementarily equivalent 1

Σ- 1

Elementary embedding

Σ- 1

Elementary extension 1

1

Elementary substructure 1

- 1

Equiconsistence 1

Filter 1

η-complete 1

– nonprincipal 1

Forcing

– Almost disjoint 1

– clumpy 1

– Cohen 1

– iterated 1

– Lévy collapsing 1

– product 1

– random 1

– Sacks 1

– Sacks (over ramified analytic hierarchy) 1

– Steel 1

Formula

Δ0 1

Δn 1

Π 1

Πn 1

Σ 1

Σn 1

– ranked 1

Function

– degree invariant 1

– increasing on an upper cone 1

– monotonic 1

– order preserving 1

– pressdown 1

– progressive 1

– uniformly degree invariant 1

Gandy topology 1

Gödel number 1

Gödel primitively recursive operators 1

Graph 1

Homogeneity

ω- 1

Hyperjump 1

Kleene-Brouwer ordering <KB 1

Locally countable partial ordering 1

Lowness 1

Master code

Σn- 1

Minimal cover 1

Model

ω- 1

– nicely coding ω- 1

Name 1

Norm 1

Ordinal

– constructive 1

– recursive 1

Ordinal definable 1

– hereditarily 1

Plain Kolmogorov Complexity 1

Predicate

1

1

1

1

1

1

– analytical 1

– arithmetical 1

– partial recursive 1

– recursive 1

Prefix-free Kolmogorov Complexity 1

Prefix-free machine 1

Projectum

Σn- 1

Property (K) 1

Random real 1

Randomness

L- 1

Γ- 1

Γ-Kurtz- 1

Γ-ML- 1

n- 1

– Kurtz 1

– Martin-Löf 1

– Schnorr 1

– Strong Γ-ML- 1

– Strong Martin-Löf 1

Rank 1

Real

-dominated 1

-traceable 1

-traceable 1

– Cohen-generic 1

– hyperarithmetic 1

–semi--traceable 1

–semi--traceable 1

Recursive language 1

Recursive structure 1

Recursive theory 1

Recursively enumerable (r.e.) 1

Recursively traceable 1

Reduction

– ≤h 1

1

Relation

– confinally progressive 1

Set

E-closed 1

H- 1

X-definable 1

1

1

1

1

1

- 1

– cofinal 1

– constructible 1

– dense 1

– extensional 1

– Friedman 1

– generic 1

– hereditarily finite 1

– inductively definable 1

– perfect 1

– pointed 1

– Prefix-free 1

– projective 1

– thin- 1

– transitive 1

– uniformly pointed 1

Shoenfield absoluteness 1

Singleton

Γ- 1

Standard part 1

Test

– Generalized Martin-Löf 1

– Kurtz 1

– Martin-Löf 1

– Schnorr 1

Theorem

– Gandy’s basis 1

– Kreisel’s basis 1

– Spector–Gandy’s- 1

– van-Lambalgen 1

Turing determinacy 1

Γ- 1

Ultrafilter 1

Uniformization 1

Upper semilattice 1

Zero sharp 1