58Ehrenfeucht, A., and A. Mostowski, A. 1956. “Models <strong>of</strong> axiomatic theories admittingautomorp<strong>his</strong>ms”. Fundamenta Mathematica 43. 50-68.Ehrenfeucht, A., and J. Mycielski, J. 1971. “Abbreviating pro<strong>of</strong>s by adding newaxioms”. Bulletin <strong>of</strong> the American Mathematical Society 77, 366-367, 1971.Feferman, S. 1964,68. “Systems <strong>of</strong> predicative analysis I,II”. Journal <strong>of</strong> Symbolic logic 29(1964), 1-30; 33 (1968), 193-220.Feferman, S. 1960. “Arithmetizati<strong>on</strong> <strong>of</strong> mathematics in a general setting”. FundamentaMathematica, 49, 35-92.Feferman, S. 1998. In the Light <strong>of</strong> Logic. Logic and Computati<strong>on</strong> in Philosophy. Oxford:Oxford University Press, 1998.Feferman, S. 2004. “Tarski's c<strong>on</strong>ceptual analysis <strong>of</strong> semantical noti<strong>on</strong>s”. Sémantique etépistémologie (A. Benmakhlouf, ed.) Editi<strong>on</strong>s Le Fennec, Casablanca (2004)[distrib. J. Vrin, Paris], 79-108, 2004/http://math.stanford.edu/~feferman/papers.htmlFolina, J. 1992. Poincaré and the Philosophy <strong>of</strong> <strong>Mathematics</strong>. L<strong>on</strong>d<strong>on</strong>: Macmillan.Friedman, H. 1971. “Higher set theory and mathematical practice”. Ann. Math. Logic, 2,325-357.Friedman, H. 1973. “The c<strong>on</strong>sistency <strong>of</strong> classical set theory relative to a set theory withintuiti<strong>on</strong>istic logic”. Journal <strong>of</strong> Symbolic Logic 38, 314-319.Friedman, H. 1978. “Classical and intuiti<strong>on</strong>istically provably recursive functi<strong>on</strong>s”. In:G.H. Müller and D.S. Scott (eds.), Higher Set Theory, Lecture Notes in <strong>Mathematics</strong>,Vol. 669, Berlin: Springer, 21-27.Friedman, H. 1979. “On the c<strong>on</strong>sistency, completeness, and correctness problems”.Ohio State University, 1979, 10 pages, unpublished.Friedman, H. 1981. “On the Necessary Use <strong>of</strong> Abstract Set Theory”. Advances in Math.,
59Vol. 41, No. 3, September pp. 209-280.Friedman, H. 1998. “Finite Functi<strong>on</strong>s and the Necessary Use <strong>of</strong> Large Cardinals”,Annals <strong>of</strong> Math., Vol. 148, No. 3, 1998, pp. 803-893.Friedman, H. 1999. “A Complete Theory <strong>of</strong> Everything: satisfiability in the universaldomain”. October 10, 1999, 14 pages, http://www.math.ohiostate.edu/%7Efriedman/Friedman, H. 2001. "Subtle Cardinals and Linear Orderings". Annals <strong>of</strong> Pure andApplied Logic 107 (2001), 1-34.Friedman, H. 2002a. “Philosophical Problems in Logic”. Seminar notes at the Princet<strong>on</strong>Philosophy <strong>Department</strong>, September-December, 2002, 107 pages,http://www.math.ohio-state.edu/%7Efriedman/Friedman, H. 2002b. “Internal finite tree embeddings”. Reflecti<strong>on</strong>s <strong>on</strong> the Foundati<strong>on</strong>s <strong>of</strong><strong>Mathematics</strong>: Essays in h<strong>on</strong>or <strong>of</strong> Solom<strong>on</strong> Feferman, ed. Sieg, Sommer, Talcott, LectureNotes in Logic, volume 15, 62-93. Providence, Rhode Island: Associati<strong>on</strong> forSymbolic Logic.Friedman, H. 2003a. “Three quantifier sentences”. Fundamenta Mathematica, 177, 213-240.Friedman, H. 2003b. “Primitive Independence Results”. Journal <strong>of</strong> Mathematical Logic,Volume 3, Number 1, 67-83.Friedman, H. 2005. “Selecti<strong>on</strong> for Borel relati<strong>on</strong>s”. In: Logic Colloquium ’01, ed. J.Krajicek, Lecture Notes in Logic, volume 20, ASL, 151-169.Friedman H. 2006a. “271: Clarificati<strong>on</strong> <strong>of</strong> Smith article”, FOM Archives, March 22, 2006,http://www.cs.nyu.edu/pipermail/fom/2006-March/010244.htmlFriedman, H. 2006b. “272: Sigma01/optimal.” FOM Archives, March 24, 2006,http://www.cs.nyu.edu/pipermail/fom/2006-March/010260.html
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1MY FORTY YEARS ON HIS SHOULDERSbyH
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4theorem is demonstrably implied by
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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: 57Monographs, 24, Oxford: Clarendon
- 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 and 68: 67Scott, D.S. 1961. “Measurable c
- Page 69: 69389.*This research was partially