Computability theory (English Wikipedia)

Davis, Martin, ed. (2004) [1965]. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. Dover Publications, Inc. p. 84. ISBN 978-0-486-43228-1. p. 84: Kurt Gödel (1946): Tarski has stressed in his lecture (and I think justly) the great importance of the concept of general recursiveness (or Turing's computability). It seems to me that this importance is largely due to the fact that with this concept one has for the first time succeeded in giving an absolute notion to an interesting epistemological notion, i.e., one not depending on the formalism chosen.
Fairtlough, Matt; Wainer, Stanley S. (1998). "Hierarchies of Provably Recursive Functions". In Buss, Samuel R. (ed.). Handbook of Proof Theory. Elsevier. pp. 149–208. ISBN 978-0-08-053318-6.

computationalcomplexity.org (Global: low place; English: low place)

blog.computationalcomplexity.org

Fortnow, Lance Jeremy (2004-02-15). "Is it Recursive, Computable or Decidable?". Archived from the original on 2022-08-07. Retrieved 2018-03-22.

doi.org (Global: 2^nd place; English: 2^nd place)

Radó, Tibor (May 1962). "On non-computable functions". Bell System Technical Journal. 41 (3): 877–884. doi:10.1002/j.1538-7305.1962.tb00480.x.
Church, Alonzo (1936a). "An unsolvable problem of elementary number theory". American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. Reprinted in Davis 1965.
Church, Alonzo (1936b). "A note on the Entscheidungsproblem". Journal of Symbolic Logic. 1 (1): 40–41. doi:10.2307/2269326. JSTOR 2269326. S2CID 42323521. Reprinted in Davis 1965.
Turing, Alan Mathison (1937) [1936]. "On computable numbers, with an application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. 2. 42 (1): 230–265. doi:10.1112/plms/s2-42.1.230. S2CID 73712. Turing, Alan Mathison (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction" (PDF). Proceedings of the London Mathematical Society. 2. 43 (1): 544–546. doi:10.1112/plms/s2-43.6.544. Archived (PDF) from the original on 2022-07-18. Retrieved 2022-08-08. Reprinted in Davis 1965.
Soare, Robert Irving (1996). "Computability and recursion" (PDF). Bulletin of Symbolic Logic. 2 (3): 284–321. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Turing, Alan Mathison (1939). "Systems of logic based on ordinals". Proceedings of the London Mathematical Society. 2. 45 (1): 161–228. doi:10.1112/plms/s2-45.1.161. hdl:21.11116/0000-0001-91CE-3. Reprinted in Davis 1965.
Post, Emil Leon (1944). "Recursively enumerable sets of positive integers and their decision problems". Bulletin of the American Mathematical Society. 50 (5): 284–316. doi:10.1090/S0002-9904-1944-08111-1. MR 0010514. Reprinted in Davis 1965.
Shore, Richard Arnold; Slaman, Theodore Allen (1999). "Defining the Turing Jump". Mathematical Research Letters. 6 (6): 711–722. doi:10.4310/mrl.1999.v6.n6.a10. ISSN 1073-2780. MR 1739227.
Ambos-Spies, Klaus; Fejer, Peter A. (2014). "Degrees of unsolvability" (PDF). In Siekmann, Jörg H. (ed.). Computational Logic. Handbook of the History of Logic. Vol. 9. Amsterdam: Elsevier/North-Holland. pp. 443–494. doi:10.1016/B978-0-444-51624-4.50010-1. ISBN 978-0-444-51624-4. MR 3362163. Archived from the original (PDF) on 2013-04-20.
Harrington, Leo Anthony; Soare, Robert Irving (1991). "Post's Program and incomplete recursively enumerable sets". Proceedings of the National Academy of Sciences USA. 88 (22): 10242–10246. Bibcode:1991PNAS...8810242H. doi:10.1073/pnas.88.22.10242. PMC 52904. PMID 11607241.
Soare, Robert Irving (1974). "Automorphisms of the lattice of recursively enumerable sets, Part I: Maximal sets". Annals of Mathematics. 100 (1): 80–120. doi:10.2307/1970842. JSTOR 1970842.
Slaman, Theodore Allen; Woodin, William Hugh (1986). "Definability in the Turing degrees". Illinois Journal of Mathematics. 30 (2): 320–334. doi:10.1215/ijm/1256044641. MR 0840131.
Kummer, Martin (1992). "A Proof of Beigel's Cardinality Conjecture". The Journal of Symbolic Logic. 57 (2): 677–681. doi:10.2307/2275299. JSTOR 2275299.
Tantau, Till (2005). "Weak Cardinality Theorems". The Journal of Symbolic Logic. 70 (3): 861–878. doi:10.2178/jsl/1122038917. JSTOR 27588397.
Orponen, Pekka (1997). "A Survey of Continuous-Time Computation Theory". Advances in Algorithms, Languages, and Complexity. pp. 209–224. doi:10.1007/978-1-4613-3394-4_11. ISBN 978-1-4613-3396-8.
Moore, Cris (1996). "Recursion theory on the reals and continuous-time computation". Theoretical Computer Science. 162 (1): 23–44. doi:10.1016/0304-3975(95)00248-0.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Turing, Alan Mathison (1939). "Systems of logic based on ordinals". Proceedings of the London Mathematical Society. 2. 45 (1): 161–228. doi:10.1112/plms/s2-45.1.161. hdl:21.11116/0000-0001-91CE-3. Reprinted in Davis 1965.

jstor.org (Global: 23^rd place; English: 15^th place)

Church, Alonzo (1936a). "An unsolvable problem of elementary number theory". American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045. Reprinted in Davis 1965.
Church, Alonzo (1936b). "A note on the Entscheidungsproblem". Journal of Symbolic Logic. 1 (1): 40–41. doi:10.2307/2269326. JSTOR 2269326. S2CID 42323521. Reprinted in Davis 1965.
Soare, Robert Irving (1996). "Computability and recursion" (PDF). Bulletin of Symbolic Logic. 2 (3): 284–321. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.
Soare, Robert Irving (1974). "Automorphisms of the lattice of recursively enumerable sets, Part I: Maximal sets". Annals of Mathematics. 100 (1): 80–120. doi:10.2307/1970842. JSTOR 1970842.
Kummer, Martin (1992). "A Proof of Beigel's Cardinality Conjecture". The Journal of Symbolic Logic. 57 (2): 677–681. doi:10.2307/2275299. JSTOR 2275299.
Tantau, Till (2005). "Weak Cardinality Theorems". The Journal of Symbolic Logic. 70 (3): 861–878. doi:10.2178/jsl/1122038917. JSTOR 27588397.

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

Harrington, Leo Anthony; Soare, Robert Irving (1991). "Post's Program and incomplete recursively enumerable sets". Proceedings of the National Academy of Sciences USA. 88 (22): 10242–10246. Bibcode:1991PNAS...8810242H. doi:10.1073/pnas.88.22.10242. PMC 52904. PMID 11607241.

pubmed.ncbi.nlm.nih.gov

Harrington, Leo Anthony; Soare, Robert Irving (1991). "Post's Program and incomplete recursively enumerable sets". Proceedings of the National Academy of Sciences USA. 88 (22): 10242–10246. Bibcode:1991PNAS...8810242H. doi:10.1073/pnas.88.22.10242. PMC 52904. PMID 11607241.

nyu.edu (Global: 1,362^nd place; English: 822^nd place)

cs.nyu.edu

Simpson, Stephen George (1998-08-24). "What is computability theory?". FOM email list. Archived from the original on 2021-12-18. Retrieved 2006-01-09.
Friedman, Harvey (1998-08-28). "Renaming recursion theory". FOM email list. Archived from the original on 2022-03-01. Retrieved 2006-01-09.

ox.ac.uk (Global: 541^st place; English: 356^th place)

web.comlab.ox.ac.uk

Turing, Alan Mathison (1937) [1936]. "On computable numbers, with an application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. 2. 42 (1): 230–265. doi:10.1112/plms/s2-42.1.230. S2CID 73712. Turing, Alan Mathison (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction" (PDF). Proceedings of the London Mathematical Society. 2. 43 (1): 544–546. doi:10.1112/plms/s2-43.6.544. Archived (PDF) from the original on 2022-07-18. Retrieved 2022-08-08. Reprinted in Davis 1965.

scottaaronson.blog (Global: low place; English: low place)

Aaronson, Scott (2025-06-28). "BusyBeaver(6) is really quite large". Shtetl-Optimized. Retrieved 2025-08-05.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Church, Alonzo (1936b). "A note on the Entscheidungsproblem". Journal of Symbolic Logic. 1 (1): 40–41. doi:10.2307/2269326. JSTOR 2269326. S2CID 42323521. Reprinted in Davis 1965.
Turing, Alan Mathison (1937) [1936]. "On computable numbers, with an application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. 2. 42 (1): 230–265. doi:10.1112/plms/s2-42.1.230. S2CID 73712. Turing, Alan Mathison (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction" (PDF). Proceedings of the London Mathematical Society. 2. 43 (1): 544–546. doi:10.1112/plms/s2-43.6.544. Archived (PDF) from the original on 2022-07-18. Retrieved 2022-08-08. Reprinted in Davis 1965.
Soare, Robert Irving (1996). "Computability and recursion" (PDF). Bulletin of Symbolic Logic. 2 (3): 284–321. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.

uchicago.edu (Global: 226^th place; English: 199^th place)

people.cs.uchicago.edu

Soare, Robert Irving (2011-12-22). "Computability Theory and Applications: The Art of Classical Computability" (PDF). Department of Mathematics. University of Chicago. Archived (PDF) from the original on 2022-06-30. Retrieved 2017-08-23.
Soare, Robert Irving (1996). "Computability and recursion" (PDF). Bulletin of Symbolic Logic. 2 (3): 284–321. doi:10.2307/420992. JSTOR 420992. S2CID 5894394.

umb.edu (Global: low place; English: 8,852^nd place)

cs.umb.edu

Ambos-Spies, Klaus; Fejer, Peter A. (2014). "Degrees of unsolvability" (PDF). In Siekmann, Jörg H. (ed.). Computational Logic. Handbook of the History of Logic. Vol. 9. Amsterdam: Elsevier/North-Holland. pp. 443–494. doi:10.1016/B978-0-444-51624-4.50010-1. ISBN 978-0-444-51624-4. MR 3362163. Archived from the original (PDF) on 2013-04-20.

web.archive.org (Global: 1^st place; English: 1^st place)

Soare, Robert Irving (2011-12-22). "Computability Theory and Applications: The Art of Classical Computability" (PDF). Department of Mathematics. University of Chicago. Archived (PDF) from the original on 2022-06-30. Retrieved 2017-08-23.
Turing, Alan Mathison (1937) [1936]. "On computable numbers, with an application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. 2. 42 (1): 230–265. doi:10.1112/plms/s2-42.1.230. S2CID 73712. Turing, Alan Mathison (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction" (PDF). Proceedings of the London Mathematical Society. 2. 43 (1): 544–546. doi:10.1112/plms/s2-43.6.544. Archived (PDF) from the original on 2022-07-18. Retrieved 2022-08-08. Reprinted in Davis 1965.
Ambos-Spies, Klaus; Fejer, Peter A. (2014). "Degrees of unsolvability" (PDF). In Siekmann, Jörg H. (ed.). Computational Logic. Handbook of the History of Logic. Vol. 9. Amsterdam: Elsevier/North-Holland. pp. 443–494. doi:10.1016/B978-0-444-51624-4.50010-1. ISBN 978-0-444-51624-4. MR 3362163. Archived from the original (PDF) on 2013-04-20.
Fortnow, Lance Jeremy (2004-02-15). "Is it Recursive, Computable or Decidable?". Archived from the original on 2022-08-07. Retrieved 2018-03-22.
Simpson, Stephen George (1998-08-24). "What is computability theory?". FOM email list. Archived from the original on 2021-12-18. Retrieved 2006-01-09.
Friedman, Harvey (1998-08-28). "Renaming recursion theory". FOM email list. Archived from the original on 2022-03-01. Retrieved 2006-01-09.

wikidata.org (Global: 10^th place; English: 98^th place)

Ershov, Yury Leonidovich; Goncharov, Sergei Savostyanovich [at Wikidata]; Nerode, Anil; Remmel, Jeffrey B. (1998). Handbook of Recursive Mathematics. North-Holland. ISBN 0-7204-2285-X.

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Shore, Richard Arnold; Slaman, Theodore Allen (1999). "Defining the Turing Jump". Mathematical Research Letters. 6 (6): 711–722. doi:10.4310/mrl.1999.v6.n6.a10. ISSN 1073-2780. MR 1739227.

Computability theory (English Wikipedia)

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