Logic
in [Science]
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CANTOR DISPROOF <<<<<<<<<<<<<<<< Hypothesis: a real number contains a finite sequence that is not computable. Contradiction Therefore: all digits of every real are contained in the list of computable reals. _________________________________________________________________ This may not IMPLY that all infinite digit sequences are computable,... 7 Jul 2010 13:29
Muddled query about models of ZF. As it says, this may be a stupid query. Be gentle. 1st-order PA has many models. But it seems to me that there is a very clear "minimal model", in that the standard model is (isomorphic to) a subset of any other model. And I gather that this fact can be proved with a fairly trivial extension of PA itself, ext... 28 Jun 2010 12:50
Solomon Feferman's notion of the "unfolding" of ZF In http://math.stanford.edu/~feferman/papers/unfolding.pdf Feferman gives a sense in which Mahlo cardinals can be seen as part of an "unfolding" of ZF in a similar sense to that in which predicative analysis is the "unfolding" of PA. However he only permits reflection formulas in which the class variables a... 20 Jun 2010 10:11
THE CANTOR ARGUMENT SO FAR ------------------------SCI.MATH----------------------------- Take any list of reals 123 456 789 Diag = 159 AntiDiag = 260 It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. ---------------------------HERC------------------------------ defn(herc_cant_3) The list of computable reals contains eve... 22 Jun 2010 20:28
WHY LIGHT IS SO OFTEN REDSHIFTED On Jun 18, 12:50 am, Pentcho Valev <pva...(a)yahoo.com> wrote: According to Newton's emission theory of light, light slows down in the gravitational field of the emitter and continues to move REDSHIFTED in the distant (zero-field) space with a DECREASED speed c'=c(1+phi/c^2), where phi is the gravitational po... 20 Jun 2010 11:16
-> Higher Infinities On 19 Jun., 11:38, "|-|ercules" <radgray...(a)yahoo.com> wrote: [ An AD(n) = (L(n,n) + 1) mod 9 -> An AD(n) =/= L(n,n) ] -> Higher Infinities Does anyone agree with the above version of Cantor's proof? Herc -- "And God posted an angel with a flaming sword at the gates of Cantor's paradise, that ... 21 Jun 2010 23:36
question on rules of inference in ZFC "David C. Ullrich" wrote: No, it is not true that FOL includes inference rules. Because you are taking a "logic" to be a set of formulae (or perhaps sentences)? -- I can't go on, I'll go on. ... 29 Jun 2010 10:45
[ An AD(n) = (L(n,n) + 1) mod 9 -> An AD(n) =/= L(n,n) ] -> Higher Infinities [ An AD(n) = (L(n,n) + 1) mod 9 -> An AD(n) =/= L(n,n) ] -> Higher Infinities Does anyone agree with the above version of Cantor's proof? Herc -- "And God posted an angel with a flaming sword at the gates of Cantor's paradise, that the slow-witted and the deliberately obtuse might not glimpse the wonder... 19 Jun 2010 05:52
A reformulation of ZF-Reg. After I made a reformulation of Z-Reg. as I presented in the post to this Usenet under the title_ A=Z-Regularity. The following is a parallel formulation but of ZF-Regularity instead of Z-Reg. A" is the set of all sentences (entailed from FOL with identity and membership) by the following non logical axioms: (... 18 Jun 2010 23:27
A=Z-Regularity. A is the set of all sentences(entailed from FOL with identity "=" and membership "e") by the following non logical axioms: (1) Comprehension: for n=0,1,2,3,...; if phi(y,w1,...,wn) is a formula in which y,w1,...,wn *are* its sole free variables and in which x is not free,then Aw1...wn Ar As E!x Ay ( y e x <-... 18 Jun 2010 17:59 |