Answer by Hello for Forcing and new ordinals
I think Paul Cohen has a decent (retrospective) justification in Section 2, Chapter IV of his book "Set Theory and the Continuum Hypothesis". Check out the Corollary on page 110 and the discussion...
View ArticleAnswer by Joel David Hamkins for Forcing and new ordinals
We don't insist on this as a prior goal. Rather, it just happens to be the case that forcing does not add new ordinals, whether you would want it to or not. Thus, this is a feature of forcing rather...
View ArticleForcing and new ordinals
$\textbf{Question}$: In expositions to forcing, why do we insist on not adding new ordinals to a countable transitive model $M$ of ZFC? For example, after ruling out transitive proper class models as...
View ArticleAnswer by Thomas Benjamin for Forcing and new ordinals
You might consider the following quote from Cohen's paper, "The Discovery of Forcing", Rocky Mountain Journal of Mathematics, Volume 32, number 4, 2002, pg. 1091 (found under title on the Web):So we...
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