Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_
Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_ Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_
possible collapse of contemporary mathematics 85exponentiable numbers is closed under exponentiation. And superexponentiation leadsus entirely away from the world of counting numbers.The belief that exponentiation, superexponentiation, and so forth, applied to numeralsyield numerals is just that – a belief. Here we have the third, and most serious,warning sign of trouble in contemporary mathematics.
- Page 148: archimedes and aristotle 59Italicus
- Page 152: combinatorics and infinity 61Figure
- Page 156: euler and infinity 63primes is infi
- Page 160: set theory 65This view leads right
- Page 164: geometry, infinity, and the peano c
- Page 168: a success of set theory 69A fundame
- Page 172: the turing machine and the busy bea
- Page 176: the infinite in the finite: p versu
- Page 180: eferences 75Gamow, G. 1947. One, Tw
- Page 184: possible collapse of contemporary m
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- Page 204: PART THREETechnical Perspectives on
- Page 210: 90 the realm of the infiniteour col
- Page 214: 92 the realm of the infinitethat th
- Page 218: 94 the realm of the infinitethat co
- Page 222: 96 the realm of the infinitefor whi
- Page 226: 98 the realm of the infiniteThis mu
- Page 230: 100 the realm of the infiniteMoreov
- Page 234: 102 the realm of the infiniteThis t
- Page 238: 104 the realm of the infinitesets)
- Page 242: 106 the realm of the infinite4.4.1
- Page 246: 108 the realm of the infiniteBut on
possible collapse of contemporary mathematics 85exponentiable numbers is closed under exponentiation. And superexponentiation leadsus entirely away from the world of counting numbers.The belief that exponentiation, superexponentiation, and so forth, applied to numeralsyield numerals is just that – a belief. Here we have the third, and most serious,warning sign of trouble in contemporary mathematics.
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