I suppose that you also think that a union of ZFC+CH and ZFC+~CH theories is an inconsistent theory. Yet according to Hamkins the worlds defined by these two theories are parts of a consistent multiverse. — litewave
It is as if you took these two statements:
(1) "This ball is red."
and
(2) "This ball is not red."
and concluded that these statements are contradictory. But you didn't notice that these statements are not about the same ball but about two different balls and thus there is no contradiction between them. — litewave
Hamkins points out that we are free to work separately in different models. He doesn't say that we combine a model of ZFC+CH with a model of ZFC+~CH. — TonesInDeepFreeze
No, he mentions that there are separate universes. That is the multiverse. The collection of separate individual universes. He doesn't combine universes all into one big clump. — TonesInDeepFreeze
And there is no "the world of ZFC+CH" or "the world of ZFC+~CH". Rather, for each set theory, there are many non-isomorphic models. — TonesInDeepFreeze
But there does not exist any model of ZFC+CH+~CH, since inconsistent theories do not have models. — TonesInDeepFreeze
"Clump"? Is that supposed to be another technical term? — litewave
Then there are "CH worlds" and "~CH worlds". — litewave
You are missing the point, which is that a set with cardinality between naturals and reals exists in the multiverse. — litewave
Then the multiverse is a model of what? Or what is it? — litewave
No, you are missing the point that such a set exists in some models in the multiverse and not in other models of the multiverse. — TonesInDeepFreeze
I already told you. It a collection of models (or "worlds" informally). — TonesInDeepFreeze
where did you get that? — litewave
whether you call the multiverse a model or a collection of models — litewave
the fact remains that a set with cardinality between naturals and reals exists in this collection — litewave
although it doesn't exist in all its subcollections (models), which is fine. And the same applies to the existence of any set that is defined by a consistent axiomatized set theory; that's why I said that all logically possible (consistent) collections exist. — litewave
Sets exist in universes (domains of discourses) for model. The collection is a collection of models. The only things that exist in that collection are models. The set exists in the universe of one of the members of the collection. — TonesInDeepFreeze
What do you think set theory is?
What do you think is an inconsistent theory (You claim ZFC+CH+~CH is not an inconsistent theory, so it's clear you don't know what an inconsistent theory is.)
What do you think a model of set theory is? — TonesInDeepFreeze
The 1986 remake as the classic?
I grieve for my people. — Banno
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