Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-29T09:31:37.544Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  24 March 2017

Gerald E. Sacks
Affiliation:
Harvard University, Massachusetts
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aczel, P, Richter, W (1972) Inductive definitions and analogues of large cardinals. In: Conference in Math. Log., London 1970. Springer, Berlin Heidelberg New York, p 1–9
Bailey, C (1984) Beta-degrees for weakly inadmissible sets. Ph.D. Thesis, Harvard University, Cambridge, MA
Barwise, J (1979) Admissible sets and structures. Springer, Berlin Heidelberg New York
Cenzer, D (1976) Monotonic inductive definitions over the continuum J. Symb. Log. 41: 188–198 Google Scholar
Chong, CT, Lerman, M (1976) Hyperhypersimple α-r.e. sets. Ann. Math. Log. 9: 1–42 Google Scholar
Chong, CT (1979) Generic sets and minimal α-degrees, Trans. Amer. Math. Soc. 254: 157–169 Google Scholar
Chong, CT (1984) Techniques of Admissible Recursion Theory. Springer, Berlin Heidelberg New York
Church, A, Kleene, SC (1937) Formal definitions in the theory of ordinal numbers. Fund. Math. 28: 11–21 Google Scholar
Dekker, JCE (1954) A theorem on hypersimple sets. Proc. Amer. Math. Soc. 5: 791–796 Google Scholar
Devlin, K (1984) Constructibility. Springer, Berlin Heidelberg New York
Driscoll, GC Jr. (1968) Metarecursively enumerable sets and their metadegrees, J. Symb. Log. 33: 389–411 Google Scholar
Feferman, S, Spector, C (1962) Incompleteness along paths in progressions of theories. J. Symb. Log. 27: 383–390 Google Scholar
Feferman, S (1965) Some applications of the notions of forcing and generic sets. Fund. Math. 56: 325–345 Google Scholar
Fenstad, JE (1980) General recursion theory. Springer, Berlin Heidelberg New York
Friedberg, R (1957a) A criterion for completeness of degrees of unsolvability, J. Symb. Log. 22:159–160 Google Scholar
Friedberg, R (1957b) Two recursively enumerable sets of incomparable degrees of unsolvability. Proc. Nat. Acad. Sci. USA 43: 236–238
Friedman, SD (1976) Recursion on Inadmissible Ordinals. Ph.D. Thesis, Massachusetts Institute of TechnologyGoogle Scholar
Friedman, SD, Sacks, GE (1977) Inadmissible recursion theory, Bull. Math. Soc. 83: 255–256 Google Scholar
Friedman, SD (1979) βrecursion theory. Trans. Amer. Math. Soc. 255: 173–200 Google Scholar
Friedman, SD (1981a) Uncountable admissibles II: compactness. Israel J. Math. 40: 129–149 Google Scholar
Friedman, SD (1981b) Negative solutions to Post's problem. II. Ann. Math. 113: 25–43
Gandy, RO (1960) Proof of Mostowski's conjecture. Bull. Acad. Polon. Sci. Math. 8: 571–575 Google Scholar
Gandy, RO (1967) General recursive functionals of finite type and hierarchies of functionals. Ann. Fac. Sci. Univ. Clermont-Ferrand 35: 202–242 Google Scholar
Gandy, RO, Sacks, GE (1967) A minimal hyperdegree, Fund. Math. 61: 215–223 Google Scholar
Green, J (1974) Σ1 compactness for next admissible sets. J. Symb. Log. 39: 105–116 Google Scholar
Griffor, ER (1980) E-Recursively Enumerable Degrees. Ph.D. Thesis, Massachusetts Institute of TechnologyGoogle Scholar
Griffor, ER, Normann, D (1982) Effective confinalities and admissibility in Erecursion. Preprint, University of Oslo
Grilliot, T (1969) Selection functions for recursive functionals. Notre Dame Jour. Formal Log. p. 225–234 Google Scholar
Harrington, L (1973) Contributions to recursion theory, in higher types. Ph.D. Thesis, (Massachusetts Institute of Technology, Cambridge MA)
Harrington, L, MacQueen, D (1976) Selection in abstract recursion theory, J. Symb. Log. 41: 153–158 Google Scholar
Hinman, P (1978) Recursion–Theoretic Hierarchies. Springer, Berlin Heidelberg New York
Homer, S, Sacks, GE (1983) Inverting the half-jump. Trans. Amer. Math. Soc. 278: 317–331 Google Scholar
Hoole, T (1982) Abstract extended 2-sections. Ph.D. thesis, Oxford University (Note: the date and title of this reference are approximate.)
Jech, T (1978) Set Theory. Academic Press, New York
Jockusch, C, Simpson, S (1976) A degree-theoretic definition of the ramified analytical hierarchy, Ann. Math. Log. 10: 1–32 Google Scholar
Kleene, SC (1943) Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53: 41–73 Google Scholar
Kleene, SC (1952) Introduction to Metamathematics. Van Nostrand, New York.
Kleene, SC (1955a) Arithmetical predicates and function quantifies, Trans. Amer. Math. Soc. 79:312–340
Kleene, SC (1955b) Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61: 193–213 Google Scholar
Kleene, SC (1955c) On the forms of the predicates in the theory of constructive ordinals II, Amer. J. Math. 77: 405–428 Google Scholar
Kleene, SC (1959) Recursive functionals and quantifies of finite types I. Trans. Amer. Math. Soc. 91:1–52
Kleene, SC (1963) Recursive functionals and quantifies of finite types II, Trans. Amer. Math. Soc. 108: 106–142 Google Scholar
Kreisel, G (1961) Set theoretic methods suggested by the notion of potential totality. In: Infinitistic Methods. Pergamon, Oxford, 325–369
Kreisel, G (1962) The axiom of choice and the class of hyperarithmetic functions, Indag. Math. 24: 307–319 Google Scholar
Kreisel, G, Sacks, GE (1963) Metarecursive sets I, II (abstracts), J. Symb. Log. 28: 304–305 Google Scholar
Kreisel, G (1965) Model-theoretic invariants: applications to recursive and hyperarithmetic operations. In: Theory of models. North-Holland, Amsterdam, p 190–205
Kreisel, G, Sacks, GE (1965) Metarecursive sets, J. Symb. Log. 30 p 318–338 Google Scholar
Kreisel, G (1971) Some reasons for generalizing recursion theory. In: Logic Colloquium ’69. North-Holland Amsterdam, p 139–198
Kripke, S (1964) Transfinite recursion on admissible ordinals I, II (abstracts), J. Symb. Log. 29:161–162 Google Scholar
Lachlan, AH (1966) Lower bounds for pairs of recursively enumerable degrees. Proc. London Math. Soc. 16: 537–569 Google Scholar
Lachlan, AH (1975) A recursively enumerable degree which will not split over all lesser ones. Ann. Math. Log. 9: 307–365 Google Scholar
Levy, A (1963) Transfinite computability (abstract), Notices Amer. Math. Soc. 10: 286 Google Scholar
Lerman, M, Sacks, GE (1972) Some minimal pairs of αrecursively enumerable degrees. Ann. Math. Log. 4: 415–42 Google Scholar
Lerman, M (1974) Maximal α-r.e. sets. Trans. Amer. Math. Soc. 188: 341–386 Google Scholar
Lerman, M (1983) Degrees of unsolvability. Springer, Berlin Heidelberg New York
Louveau, A (1980) A separation theorem for Σ1 1 sets, Trans. Amer. Math. Soc. 260: 363–378 Google Scholar
Maass, W (1977a) Minimal pairs and minimal degrees in higher recursion theory. Zeit. Math. Logik 18: 169–186 Google Scholar
Maass, W (1977b) Contributions to α- and βrecursion theory. Habilitationsschrift, Universität München
Maass, W (1978a) The uniform regular set theorem in arecursion theory. J. Symb. Log. 43: 270–279 Google Scholar
Maass, W (1978b) Inadmissibility, tame r.e. sets and the admissible collapse. Ann. Math. Log. 13: 149–170 Google Scholar
Machover, M (1961) The theory of transfinite recursion. Bull. Amer. Math. Soc. 67: 575–578
Machtey, M (1970) Admissible ordinals and intrinsic consistency. J. Symb. Log. 35: 389–400 Google Scholar
Macintyre, JM (1968) Contributions to metarecursion theory. Ph.D. Thesis, M.I.T., Cambridge MA
Macintyre, JM (1973) Minimal αrecursion theoretic degrees. J. Symb. Log. 38: 18–28 Google Scholar
MacQueen, D (1972) Recursion in finite types. Ph.D. Thesis. M.I.T., Cambridge MA
Moldstad, J (1977) Computations in higher types. Lecture Notes in Math. 574. Springer, Berlin Heidelberg New York
Moschovakis, YN (1966) Many-one degrees of the Ha(x) predicates. Parif. Jour. Math. 18: 329–342 Google Scholar
Moschovakis, YN (1980) Descriptive set theory. North-Holland, Amsterdam
Muchnik, AA (1956) On the unsolvability of the problem of reducibility in the theory of algorithms. Dokl. Akad. Nauk SSSR, N.S. 108: 194–197 Google Scholar
Normann, D (1974) Imbedding of higher type theories. Preprint Series in Math. 16: Oslo
Normann, D (1975) Degrees of functionals. Preprint Series in Math. 22: Oslo
Normann, D (1978a) Set recursion. In: Generalized recursion theory II. North-Holland, Amsterdam, 303–320
Normann, D (1978b) Recursion in 3 E and a splitting theorem. In: Essays on mathematical and philosophical logic. D. Reidel, Dordrecht, p 275–285
Ohashi, K (1970) On a question of G.E. Sacks. J. Symb. Log. 35: 46–50 Google Scholar
Owings, JC Jr. (1969) Π1 1-sets, ω-sets and metacompleteness. J. Symb. Log. 34: 194–204 Google Scholar
Platek, R (1966) Foundations of recursion theory, Ph.D. Thesis. Stanford University, Stanford CA
Post, EL (1944) Recursively enumerable sets of positive integers and their decision problems. Bull. Amer. Math. Soc. 50: 284–316 Google Scholar
Richter, W (1967) Constructive transfinite number classes. Bull. Amer. Math. Soc. 73: 261–265 Google Scholar
Rogers, H Jr. (1967) Theory of recursive functions and effective computability. McGraw-Hill, New York
Sacks, GE (1963a) Recursive enumerability and the jump operator. Trans. Amer. Math. Soc. 108: 223–239 Google Scholar
Sacks, GE (1963b) On the degrees less than 0′. Annals of Math. 77: 211–231 Google Scholar
Sacks, GE (1964) The recursively enumerable degrees are dense. Ann. of Math. 80: 193–205 Google Scholar
Sacks, GE (1966) Post's problem, admissible ordinals and regularity. Trans. Amer. Math. Soc. 124:1–23 Google Scholar
Sacks, GE (1969) Measure theoretic uniformity in recursion theory and set theory. Trans. Amer. Math. Soc. 142: 381–420 Google Scholar
Sacks, GE (1970) Recursion in objects of finite type. Proc. Internat. Cong. Math. 1: 251–254 Google Scholar
Sacks, GE (1971) Forcing with perfect closed sets. In Axiomatic set theory, Proc. Symposia in Pure Math. Amer. Math. Soc. 13: 331–355 Google Scholar
Sacks, GE, Simpson, S (1972) The α-finite injury method. Ann. Math. Log. 4: 343–367 Google Scholar
Sacks, GE (1974) The 1-section of a type n-object. In: Generalized recursion theory. North-Holland, Amsterdam, p 81–96
Sacks, GE (1976) Countable admissible ordinals and hyperdegrees. Advances in Math. 19: 213–262 Google Scholar
Sacks, GE (1977) The k-section of a type n-object. Amer. J. Math. 99: 901–917 Google Scholar
Sacks, GE (1980) Post's problem, absoluteness and recursion in finite types. In The Kleene Symposium, North-Holland, Amsterdam, p 201–222
Sacks, GE (1985) Post's problem in Erecursion. In Proceedings of symposia in pure mathematics. Amer. Math. Soc. 42: 177–193 Google Scholar
Sacks, GE (1986) On the limits of E-recursive enumerability. Ann. of Pure and Applied Logic 31: 87–120 Google Scholar
Sacks, GE, Slaman, TA (1987) Inadmissible forcing. Advances in Math. 66: 1–30 Google Scholar
Sacks, GE (199?) Set forcing over E-closed structures (to appear)Google Scholar
Shore, RA (1974) Σ n sets which are ∆ n incomparable (uniformly). J. Symb. Log. 39: 295–304 Google Scholar
Shore, RA (1975a) The irregular and non-hyperregular α-r.e. degrees, Israel J. Math. 22: 28–411 Google Scholar
Shore, RA (1975b) Splitting an αrecursively enumerable set. Trans. Amer. Math. Soc. 204: 65–78 Google Scholar
Shore, RA (1975c) Some more minimal pairs of arecursively enumerable degrees (abstract). Notices Amer. Math. Soc. 22: A524–525 Google Scholar
Shore, RA (1976a) The recursively enumerable α-degrees are dense. Ann. Math. Log. 9: 123–155 Google Scholar
Shore, RA (1976b) Combining the density and splitting theorem for α-r.e. degrees (abstract). Notices Amer. Math. Soc. 23: A598 Google Scholar
Simpson, SG (1971) Admissible Ordinals and Recursion Theory. Ph.D. Thesis, M.I.T., Cambridge MA
Simpson, SG (1974a) Degree theory on admissible ordinals. In Generalized recursion theory, Proceedings of the 1972 Oslo Symposium. North-Holland, Amsterdam, p 165–194
Simpson, SG (1974b) Post's problem for admissible sets. In Generalized recursion theory, Proceedings of the 1972 Oslo Symposium, North-Holland, Amsterdam, p 437–441
Slaman, TA (1981) Aspects of E-Recursion. Ph.D. Thesis. Harvard University, Cambridge MA
Slaman, TA (1983) The extended plus-one hypothesis–a relative consistency result. Nagoya Math. J. 92: 107–120 Google Scholar
Slaman, TA (1985a) Reflection and forcing in Erecursion theory. Ann. Pure Appl. Log. 29: 79–106 Google Scholar
Slaman, TA (1985b) The Erecursively enumerable degrees are dense. In Proceedings of symposia in pure mathematics. Amer. Math. Soc. 42, 195–213 Google Scholar
Soare, RI (1987) Recursively enumerable sets and degrees. Springer, Berlin Heidelberg New York
Spector, C (1955) Recursive well-orderings, J. Symb. Log. 20: 151–163 Google Scholar
Spector, C (1956) On degrees of recursive unsolvability, Ann. of Math. 64: 581–592 Google Scholar
Spector, C (1959) Hyperarithmetic quantifiers, Fund. Math. 48: 313–320 Google Scholar
Stoltenberg-Hansen, V (1977) Finite injury argument in infinite computation theories. Preprint Series in Math. 12: Oslo
Suzuki, Y (1964) A complete classification of the Δ1 2 functions, Bull. Amer. Math. Soc. 70: 246–253 Google Scholar
Takeuti, G (1960) On the recursive functions of ordinal numbers. J. Math. Soc. Japan 12: 119–128
Tanaka, H (1968) A basis result for Π1 1-sets of positive measure. Comment. Math. Univ. St. Paul 16: 115–127
Tugué, T (1964) On the partial recursive functions of ordinal numbers. J. Math. Soc. Japan 16: 1–31
vande, Wiele J (1982) Recursive dilators and generalized recursion. In Proceedings of the Herbrand Symposium. North-Holland, Amsterdam, p 325–332
Yang, DP (1984) On the embedding of α-recursive presentable lattices in the a-recursive degrees below 0′. J. Symb. Log. 49: 488–502 Google Scholar
Yates, CEM (1966) A minimal pair of recursively enumerable degrees. J. Symb. Log. 31: 159–168 Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bibliography
  • Gerald E. Sacks, Harvard University, Massachusetts
  • Book: Higher Recursion Theory
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316717301.020
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bibliography
  • Gerald E. Sacks, Harvard University, Massachusetts
  • Book: Higher Recursion Theory
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316717301.020
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • Gerald E. Sacks, Harvard University, Massachusetts
  • Book: Higher Recursion Theory
  • Online publication: 24 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316717301.020
Available formats
×