my forty years on his shoulders - Department of Mathematics

More documents

Recommendations

Info

6886.Tarski, A., and McKinsey, J.C.C. 1951. A decision method for elementary algebra andgeometry. 2nd revised edition (Berkeley and Los Angeles).Tarski, A. 1952. “Some notions and methods on the borderline of algebra andmetamathematics”. Proc. International Congress of Mathematicians, Cambridge,Mass. 1950, Vol. 1, Amer. Math. Soc. (Providence), 705-720.Tarski, A., Mostowski, A., and Robinson, R.M. 1953. Undecidable Theories. Amsterdam:North-Holland.Tarski, A., and Vaught, R.L. 1957. “Arithmetical extensions of relational systems”.Compositio Mathematica 13, 81-102.Wang, H. 1987. Reflections on Kurt Gödel. Cambridge, Massachusetts: MIT Press.Wang, H. 1996. A logical journey: from Gödel to philosophy. Cambridge, Massachusetts:MIT Press, 1996.Weyl, H. 1918. Das Kontinuum. Kritische Untersuchungen über die Grundlagen derAnalysis (Velt, Leipzig).Weyl, H. 1987. The Continuum. A Critical Examination of the Foundations of Analysis.English translation of Weyl (1918), by S. Pollard and T. Bole (Thomas JeffersonPress, University Press of America, Latham, distributors).Wiedijk F. 2006. (ed.), The Seventeen Provers of the World. Foreword by Dana S. Scott,Springer LNAI 3600, 2006.Williamson, T. 2000. “Existence and Contingency”. Proceedings of the AristotelianSociety, 100, pp. 117-139.Williamson, T. 2003. “Everything”. Philosophical Perspectives 17, pp. 415-465.Williamson, T. 2006. “Absolute Identity and Absolute Generality”. In: A. Rayo and G.Uzquiano, eds., Absolute Generality, (Oxford: Oxford University Press), pp. 369-
69389.*This research was partially supported by NSF Grant DMS 0245349 and by Grant#15400 from the John Templeton Foundaiton.
Page 1:
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 and 66: 65Mostowski, A. 1952. Sentences und
Page 67: 67Scott, D.S. 1961. “Measurable c
show all

my forty years on his shoulders - Department of Mathematics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?