II ch.
(Elemente) and ch. xxxiv.
While before, cg and ci came before ch, it’d now be cg, ch, then ci.
Chi, which looks like an “X,” is most often transliterated as a hard “ch,” as in “chaos.”
Melden (1979: Ch.
However, CH was left untouched.
This involves a parallel case for CH.
Despite his efforts Cantor could not resolve CH.
In 1938 Gödel proved the consistency of the CH with ZFC.
CH is known to be undecidable on the basis of the axioms in ZFC.
Nevertheless Hilbert published a (false) proof of the CH in Hilbert 1926.
For example, if ADL(ℝ) holds then this version of CH holds for all sets of real numbers in L(ℝ).
His interests also included the treatment of women (ch. 2–4) and children (ch. 5).
The above case for the failure of CH is the strongest known local case for axioms that settle CH.
The above results led Woodin to the identification of a “canonical” model in which CH fails and this formed the basis of his an argument that CH is false.
Thus, when all the dust settles the real import of Woodin's work on CH (so the argument goes) is not that CH is false but rather that CH very likely has an answer.
Creator Joe Pedott credits the idea to his home in San Francisco and an agent at his ad firm's butcher of the name, ultimately leading to its infamous jingle, "Ch-Ch-Ch-Chia!"
Notice that in the context of ZFC, these three hierarchies of versions of CH are all successive approximations of CH and in the limit case, where Γ is the pointclass of all sets of reals, they are equivalent to CH.
For a discussion of this problem, see Egan and John 2003 (Other Internet Resources); Dretske (1995, Ch. 5) argues against P3 (see also Tye 1995, 150–5; 2002, Ch. 6; Lycan 1996, 115–7; and Noë 2005, Ch. 7); P1 is denied in Chalmers 2004.
There is an asymmetry that was pointed out by Martin, namely, that a definable counterexample to CH is a real counterexample, while no matter how far one proceeds in verifying definable versions of CH at no stage will one have touched CH itself.
CH
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