Haven (graph theory): Difference between revisions

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In set theory, a discipline within mathematics, an admissible set is a transitive set $A$ such that $⟨ A, \in ⟩$ is a model of Kripke–Platek set theory (Barwise 1975).

The smallest example of an admissible set is the set of hereditarily finite sets. Another example is the set of hereditarily countable sets.

Barwise, Jon (1975). Admissible Sets and Structures: An Approach to Definability Theory, Perspectives in Mathematical Logic, Volume 7, Springer-Verlag. Electronic version on Project Euclid.

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+In [[set theory]], a discipline within mathematics, an '''admissible set''' is a [[transitive set]] <math> A\, </math> such that <math>\langle A,\in \rangle</math> is a [[model theory|model]] of [[Kripke–Platek set theory]] (Barwise 1975).
+The smallest example of an admissible set is the set of [[hereditarily finite set]]s. Another example is the set of [[hereditarily countable set]]s.
+==See also==
+* [[Admissible ordinal]]
+== References ==
+* Barwise, Jon (1975). ''Admissible Sets and Structures: An Approach to Definability Theory'', Perspectives in Mathematical Logic, Volume 7, Springer-Verlag. [http://projecteuclid.org/euclid.pl/1235418470 Electronic version] on [[Project Euclid]].
+[[Category:Set theory]]
+{{settheory-stub}}