Uncountably many R4s, 4-space is indeed unique.
http://dictionary.sensagent.com/fake+r4/en-en/
Some apps in physics
http://iopscience.iop.org/0264-9381/18/16/319;jsessionid=1695FC8278156971901894C612EAB18E.c3
Unpredictability and undecidability in dynamical systems. I don't know why this didn't get more attention.
http://prl.aps.org/abstract/PRL/v64/i20/p2354_1
http://tuvalu.santafe.edu/~moore/nonlinearity-gs.pdf
The FAT Theorem. Fuzzy systems can also be used in physics to predict, but the trade off is the lack of understanding (although studying the rule patches that work can lead to understanding).
http://sipi.usc.edu/~kosko/FuzzyUniversalApprox.pdf
Bass's proof, only one consciousness assuming QM
http://www.fredalanwolf.com/myarticles/Bass_1.pdf
Free will theorem.
http://www.ams.org/notices/200902/rtx090200226p.pdf
The Shadow Theorem (illustrates how apparently random orbits may actually be the "shadows" of deterministic motions in higher dimensional spaces).
http://books.google.com/books?id=oh7NoePgmOIC&pg=PA156&lpg=PA156&dq=shadow+theorem+fractals&source=bl&ots=PgTeIJPCh2&sig=y_bm0nE30fujqtHM4eo96mbnwwI&hl=en&ei=39AoTYqiJo2asAPF0bTJCA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBcQ6AEwAA#v=onepage&q=shadow%20theorem%20fractals&f=false
Ultimate-logic-to-infinity-and-beyond
https://www.newscientist.com/article/mg21128231-400-ultimate-logic-to-infinity-and-beyond/
