Definition of Hyperarithmetical. Meaning of Hyperarithmetical. Synonyms of Hyperarithmetical

- _{1}^{1}} . The hyperarithmetical sets are exactly the Δ 1 1 {\displaystyle \Delta _{1}^{1}} sets. The definition of hyperarithmetical sets as Δ 1 1 {\displaystyle...
- Hyperjump may refer to: Hyperjump, a function in hyperarithmetical theory, a subtopic of com****bility theory Hyperjump, a fictional hyperspace jump,...
- classifications ****igned to a formula and the set it defines. The hyperarithmetical hierarchy and the analytical hierarchy extend the arithmetical hierarchy...
- countable) Σ0 α Π0 α Σ0 α Π0 α ⋮ ⋮ Σ0 ωCK 1 = Π0 ωCK 1 = Δ0 ωCK 1 = Δ1 1 = hyperarithmetical Σ0 ω1 = Π0 ω1 = Δ0 ω1 = Δ1 1 = B = Borel Σ1 1 = lightface analytic...
- called hyperarithmetical. An alternate classification of these sets by way of iterated com****ble functionals is provided by the hyperarithmetical theory...
- set theory with those of generalized recursion theory (especially hyperarithmetical theory). In particular, it focuses on lightface analogues of hierarchies...
- been studied. The most well known are arithmetical reducibility and hyperarithmetical reducibility. These reducibilities are closely connected to definability...
- includes the study of lightface pointclasses, and is closely related to hyperarithmetical theory. In many cases, results of classical descriptive set theory...
- for example characterizations of the classes of provably recursive, hyperarithmetical, or Δ 2 1 {\displaystyle \Delta _{2}^{1}} functions of the theory...
- talk about f being com****ble in g by identifying g with its graph. Hyperarithmetical theory studies those sets that can be computed from a com****ble ordinal...