[FOM] 408: Kernel Tower Theory 2

Sat Apr 3 12:27:15 EDT 2010

I believe that most FOMers do not know and would like to know how your extremely interesting THEOREMS
involving consistency of various large cardinals over weak base theories can be proved.
If you put effort into defining notions and stating theorems, please give us, or promise to give in the future,
at least very rough feeling about the ways of PROOFS.
Any single proof would suffice.
Thank you, Jan Pax

>  
>  THEOREM 7.4. Proposition 7.3 is provable in SRP+ but not in any  
>  fragment of SRP consistent with RCA_0. Proposition 7.3 is provably  
>  equivalent to Con(SRP) over WKL_0.
>  
>  The upper shift is an example of a piecewise linear (partial) function  
>  from Q into Q. We intend to study carefully what happens when we use  
>  any finite sets of such functions, instead of just the upper shift on  
>  Q as above. We expect that we will be able to completely analyze this  
>  in SRP+. We already know that SRP does not suffice. In particular, ZFC  
>  does not suffice.
>  
>  **********************
>  
>  I use http://www.math.ohio-state.edu/~friedman/ for downloadable
>  manuscripts. This is the 408th in a series of self contained numbered
>  postings to FOM covering a wide range of topics in f.o.m. The list of
>  previous numbered postings #1-349 can be found at
>  http://www.cs.nyu.edu/pipermail/fom/2009-August/014004.html
>  in the FOM archives.
>  
>  350: one dimensional set series  7/23/09  12:11AM
>  351: Mapping Theorems/Mahlo/Subtle  8/6/09  10:59PM
>  352: Mapping Theorems/simpler  8/7/09  10:06PM
>  353: Function Generation 1  8/9/09  12:09PM
>  354: Mahlo Cardinals in HIGH SCHOOL 1  8/9/09  6:37PM
>  355: Mahlo Cardinals in HIGH SCHOOL 2  8/10/09  6:18PM
>  356: Simplified HIGH SCHOOL and Mapping Theorem  8/14/09  9:31AM
>  357: HIGH SCHOOL Games/Update  8/20/09  10:42AM
>  358: clearer statements of HIGH SCHOOL Games  8/23/09  2:42AM
>  359: finite two person HIGH SCHOOL games  8/24/09  1:28PM
>  360: Finite Linear/Limited Memory Games  8/31/09  5:43PM
>  361: Finite Promise Games  9/2/09  7:04AM
>  362: Simplest Order Invariant Game  9/7/09  11:08AM
>  363: Greedy Function Games/Largest Cardinals 1
>  364: Anticipation Function Games/Largest Cardinals/Simplified 9/7/09
>  11:18AM
>  365: Free Reductions and Large Cardinals 1  9/24/09  1:06PM
>  366: Free Reductions and Large Cardinals/polished  9/28/09  2:19PM
>  367: Upper Shift Fixed Points and Large Cardinals  10/4/09  2:44PM
>  368: Upper Shift Fixed Point and Large Cardinals/correction  10/6/09
>  8:15PM
>  369. Fixed Points and Large Cardinals/restatement  10/29/09  2:23PM
>  370: Upper Shift Fixed Points, Sequences, Games, and Large Cardinals
>  11/19/09  12:14PM
>  371: Vector Reduction and Large Cardinals  11/21/09  1:34AM
>  372: Maximal Lower Chains, Vector Reduction, and Large Cardinals
>  11/26/09  5:05AM
>  373: Upper Shifts, Greedy Chains, Vector Reduction, and Large
>  Cardinals  12/7/09  9:17AM
>  374: Upper Shift Greedy Chain Games  12/12/09  5:56AM
>  375: Upper Shift Clique Games and Large Cardinals 1graham
>  376: The Upper Shift Greedy Clique Theorem, and Large Cardinals
>  12/24/09  2:23PM
>  377: The Polynomial Shift Theorem  12/25/09  2:39PM
>  378: Upper Shift Clique Sequences and Large Cardinals  12/25/09  2:41PM
>  379: Greedy Sets and Huge Cardinals 1
>  380: More Polynomial Shift Theorems  12/28/09  7:06AM
>  381: Trigonometric Shift Theorem  12/29/09  11:25AM
>  382: Upper Shift Greedy Cliques and Large Cardinals  12/30/09  2:51AM
>  383: Upper Shift Greedy Clique Sequences and Large Cardinals 1
>  12/30/09  3:25PM
>  384: THe Polynomial Shift Translation Theorem/CORRECTION  12/31/09
>  7:51PM
>  385: Shifts and Extreme Greedy Clique Sequences  1/1/10  7:35PM
>  386: Terrifically and Extremely Long Finite Sequences  1/1/10  7:35PM
>  387: Better Polynomial Shift Translation/typos  1/6/10  10:41PM
>  388: Goedel's Second Again/definitive?  1/7/10  11:06AM
>  389: Finite Games, Vector Reduction, and Large Cardinals 1  2/9/10
>  3:32PM
>  390: Finite Games, Vector Reduction, and Large Cardinals 2  2/14/09
>  10:27PM
>  391: Finite Games, Vector Reduction, and Large Cardinals 3  2/21/10
>  5:54AM
>  392: Finite Games, Vector Reduction, and Large Cardinals 4  2/22/10
>  9:15AM
>  393: Finite Games, Vector Reduction, and Large Cardinals 5  2/22/10
>  3:50AM
>  394: Free Reduction Theory 1  3/2/10  7:30PM
>  395: Free Reduction Theory 2  3/7/10  5:41PM
>  396: Free Reduction Theory 3  3/7/10  11:30PM
>  397: Free Reduction Theory 4  3/8/10  9:05AM
>  398: New Free Reduction Theory 1  3/10/10  5:26AM
>  399: New Free Reduction Theory 2  3/12/10  9:36AM
>  400: New Free Reduction Theory 3  3/14/10  11:55AM
>  401: New Free Reduction Theory 4  3/15/10  4:12PM
>  402: New Free Reduction Theory 5  3/19/10  12:59PM
>  403: Set Equation Tower Theory 1  3/22/10  2:45PM
>  404: Set Equation Tower Theory 2  3/24/10  11:18PM
>  405: Some Countable Model Theory 1  3/24/10  11:20PM
>  406: Set Equation Tower Theory 3  3/25/10  6:24PM
>  407: Kernel Tower Theory 1  3/31/10  12:02PM
>  
>  Harvey Friedman
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