# clique idea – Can there animate such a sequence of elementary embeddings of the universe to itself? retort

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## clique idea – Can there animate such a sequence of elementary embeddings of the universe to itself?

Working in ZfC + Wholeness:

Can we maintain a countable sequence of elementary embeddings of the universe to itself, such that the ambit of every embedding is a subclass of the ambit of its successor, and such that the union of all of the ranges of these embeddings is the universe itself?

Formally can we maintain a succesful class sequence $$j`mathbb N$$ such that:

$$forall n in mathbb N : j_n: V prec V land rng(j_{n+1}) supset rng(j_n) forall x exists n in mathbb N : x in rng(j_n)$$

level to: ZfC means ZFC however with substitute restricted to absolutely the language of clique idea, i.e. it does not make use of the character $$j$$; nonetheless, $$j$$ is allowed in all situations of separation.

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