Certain very large cardinals are not created in small forcing extensions

摘要: Abstract The large cardinal axioms of the title assert, respectively, existence a nontrivial elementary embedding j : V λ → , such which is moreover Σ n 1 and extends to an + . It known that these are preserved in passing from ground model small forcing extension. In this paper reverse directions preservations proved. Also following shown (and used above proofs place using standard fact): if ZFC [ G ] P -generic extension then definable parameter δ where =