In set theory, a discipline within mathematics, an admissible set is a transitive set A {\displaystyle A\,} such that ⟨ A , ∈ ⟩ {\displaystyle \langle...

Kripke–Platek set theory. An ordinal number α {\displaystyle \alpha } is called an admissible ordinal if L α {\displaystyle L_{\alpha }} is an admissible set. L...

In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing...

In set theory, an ordinal number α is an admissible ordinal if Lα is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other...

Look up admissibility in Wiktionary, the free dictionary. Admissibility may refer to: Admissible evidence, evidence which may be introduced in a court...

considered as sets inside a maximal universe that are transitive as such are called admissible sets. Axiomatic set theory Admissible set Admissible ordinal...

generalisation of recursion theory to subsets of admissible ordinals α {\displaystyle \alpha } . An admissible set is closed under Σ 1 ( L α ) {\displaystyle...

the set of nodes expanded, not the number of node expansions (the number of iterations of A*'s main loop). When the heuristic being used is admissible but...

related sequences, e.g. the three sequences corresponding to the three admissible 8-tuples (prime octuplets), and the union of all 8-tuples. The first term...

to be the admissible sets of X . {\displaystyle X.} A field of sets ( X , F ) {\displaystyle (X,{\mathcal {F}})} is called a σ-field of sets and the algebra...

optimal control theory is to find some sequence of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to...

ω. admissible An admissible set is a model of Kripke–Platek set theory, and an admissible ordinal is an ordinal α such that Lα is an admissible set AH...

Studies in Logic and the Foundations of Mathematics Barwise, Jon (1975). Admissible Sets and Structures. Berlin: Springer-Verlag. ISBN 0-387-07451-1. Devlin...

In mathematics, admissible representations are a well-behaved class of representations used in the representation theory of reductive Lie groups and locally...

In computability theory, admissible numberings are enumerations (numberings) of the set of partial computable functions that can be converted to and from...

hyperarithmetical, and the smallest admissible ordinal after ω {\displaystyle \omega } (an ordinal α {\displaystyle \alpha } is called admissible if L α ⊨ K P {\displaystyle...

In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than...

{S}}=(a,b)} . Thus the left side of the lower boundary of the risk set is the set of admissible decision rules. A minimax Bayes rule is one that minimises the...

and science Olympiads at the national level. ——— (2016). "On the μ-admissible set in the extended affine Weyl groups of E6 and E7". Journal of Algebra...

variable in language of the theory. For example, Church's rule is an admissible rule in first-order Heyting arithmetic H A {\displaystyle {\mathsf {HA}}}...

{\displaystyle {\mathsf {KP\omega }}} is Kripke-Platek set theory, whose universe is an admissible set containing ω {\displaystyle \omega } . W − K P I {\displaystyle...

ω-models of second-order arithmetic and admissible sets (1975, p.105). Accessed 2021 November 3. W. Marek, Stable sets, a characterization of β₂-models of...

_{0}} , a fragment of Kripke-Platek set theory extended by an axiom stating every set is contained in an admissible set. Buchholz's ordinal is also the order...

case in which a landmark decision about the admissibility and authentication of digital evidence was set down in the form of a 100-page opinion by Magistrate...

if it is a maximal element (with respect to the set-theoretical inclusion) among the admissible sets with respect to S {\displaystyle S} , E {\displaystyle...

(1988). p.105 Avigad, Jeremy (May 23, 2001). "An ordinal analysis of admissible set theory using recursion on ordinal notations" (PDF). Journal of Mathematical...

More generally, the model is said to be set (or partially) identified if there exists at least one admissible s ≠ s ⋆ {\displaystyle s\neq s^{\star }}...

Truth and provability, manuscript in progress. Barwise, Jon (1976). Admissible Sets and Structures: an Approach to Definability Theory. Perspectives in...

Program has been given periodically since 2001. Barwise, K. J. (1975) Admissible Sets and Structures. An Approach to Definability Theory ISBN 0-387-07451-1...

sustained in the accident, and claimed that the blood test should not be admissible as evidence since the police did not have probable cause to obtain a blood...