[FOM] Refuting CH?/3

[Harvey Friedman]

Refuting CH?/1 was garbled. Here is a corrected version.

GENERAL PRINCIPLE. Any simple property that holds of all
simple Borel data, in fact holds of all such simple data, regardless
of whether it is Borel or not.

"THEOREM". The General Principle is consistent and refutes CH.

So here is an example. We use n below for integers.

THEOREM 1. Let f:R into R be Borel. There exist x,y such that x is
not any f(y+n) and y is not any f(x+n).

PROPOSITION 2. Let f:R into R. There exist x,y such that x is not any
f(y+n) and y is not any f(x+n).

THEOREM 3. Proposition 2 is equivalent to not CH.

Refuting CH?/2 http://www.cs.nyu.edu/pipermail/fom/2016-April/019766.html
discusses the precise versions of Borel Transfer.

BOREL TRANSFER THEORY
THE METHOD OF BOREL TRANSFER

are some names, as indicated by the three postings Refuting CH?/2,
Refuting CH?/3, Proving(?) PD.

Harvey Friedman