Permutation model: Difference between revisions

Revision as of 02:43, 9 October 2014

Revision as of 19:37, 8 February 2015

Line 10:

*Any subgroup containing an element of ''F'' is in ''F''

*Any conjugate of an element of ''F'' is in ''F''

*The subgroup fixing any element of ''A'' is in ''F''.

If ''V'' is a model of ZFA with ''A'' the set of atoms, then an element of ''V'' is called symmetric if the subgroup fixing it is in ''F'', and is called hereditarily symmetric if it and all elements of its transitive closure are symmetric. The '''permutation model''' consists of all hereditarily symmetric elements, and is a model of ZFA.

Line 21:

*{{citation|last=Fraenkel|first= A.

|title=Der Begriff “definit”"definit" und die Unabhängigkeit des Auswahlaxioms| JFM =48.0199.02

|journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften|year= 1922|pages= 253-257253–257 }}

*{{citation|first= Andrzej |last=Mostowski|title= Über den Begriff einer Endlichen Menge|year=1938|journal= Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III|volume=31|issue=8|pages=13–20}}