my forty years on his shoulders - Department of Mathematics

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1MY FORTY YEARS ON HIS SHOULDERSbyH
Page 4 and 5:
4theorem is demonstrably implied by
Page 6 and 7:
6At the outer limits, normal mathem
Page 8 and 9:
8“Thus, according to Gödel, the
Page 11 and 12:
11(Rosser 1936) is credited for sig
Page 13 and 14:
13(Davis 1973), (Matiyasevich 1993)
Page 15 and 16: 15For degree 3, the existence of an
Page 17 and 18: 17v) connectives ¬,∧,∨,→,↔
Page 19 and 20: 19PROV[x 1 /#(A)] → PROV[x 1 /PR(
Page 21 and 22: 21FORMAL SECOND INCOMPLETENESS (PA(
Page 23 and 24: 23function symbols, together with t
Page 25 and 26: 25remarks by R. Parikh, it is likel
Page 27 and 28: 27The same remarks can be made with
Page 29 and 30: 29Harrington 1977), and are proved
Page 31 and 32: 31¬ as ¬.∧ as ∧.→ as →.
Page 33 and 34: 33the result of simultaneously repl
Page 35 and 36: 35We believe that the Spector devel
Page 37 and 38: 37P.J. Cohen proved that if ZF is c
Page 39 and 40: 39My ideas are not very well develo
Page 41 and 42: 41vertices of T i .It is natural to
Page 43 and 44: 43An extremely interesting conseque
Page 45 and 46: 45THEOREM 9.5. (Friedman 2005). The
Page 47 and 48: 47Showing that all such statements
Page 49 and 50: 49in E depends only on the order ty
Page 51 and 52: 51Also consider the recursive unsol
Page 53 and 54: 53used to prove statements in and a
Page 55 and 56: 55statements represents an inevitab
Page 57 and 58: 57Monographs, 24, Oxford: Clarendon
Page 59 and 60: 59Vol. 41, No. 3, September pp. 209
Page 61 and 62: 61Friedman, H., Robertson, N., and
Page 63 and 64: 63Society, 8:437-479, 1902.Hilbert,
Page 65: 65Mostowski, A. 1952. Sentences und
Page 69: 69389.*This research was partially
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