Large countable ordinal (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Large countable ordinal" in English language version.

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7doi.org

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Buchholz, Wilfried; Feferman, Solomon; Pohlers, Wolfram; Sieg, Wilfried (1981). Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies. Lecture Notes in Mathematics. Vol. 897. Springer-Verlag, Berlin-New York. doi:10.1007/bfb0091894. ISBN 3-540-11170-0. MR 0655036.

arxiv.org

Arai, Toshiyasu (2015). "A simplified analysis of first-order reflection". arXiv:1907.17611v1.
Arai, Toshiyasu (1996). "Introducing the hardline in proof theory". arXiv:1104.1842v1 [math.LO].

cambridge.org

Simpson, Stephen G. (2009). Subsystems of Second Order Arithmetic. Perspectives in Logic (2 ed.). Cambridge: Cambridge University Press. ISBN 978-0-521-88439-6.
"Fred G. Abramson, Locally countable models of $\Sigma _{1}$ -separation" (2014). Accessed 2022 July 23.

core.ac.uk

K. J. Devlin, An introduction to the fine structure of the constructible hierarchy, Studies in Logic and the Foundations of Mathematics (vol. 79, 1974). Accessed 2022-12-04.
K. J. Devlin, An introduction to the fine structure of the constructible hierarchy (1974). Accessed 21 February 2023.

doi.org

Buchholz, W. (1986-01-01). "A new system of proof-theoretic ordinal functions". Annals of Pure and Applied Logic. 32: 195–207. doi:10.1016/0168-0072(86)90052-7. ISSN 0168-0072.
Buchholz, Wilfried; Feferman, Solomon; Pohlers, Wolfram; Sieg, Wilfried (1981). Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies. Lecture Notes in Mathematics. Vol. 897. Springer-Verlag, Berlin-New York. doi:10.1007/bfb0091894. ISBN 3-540-11170-0. MR 0655036.
Rathjen, Michael (1994-01-01). "Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM". Archive for Mathematical Logic. 33 (1): 35–55. doi:10.1007/BF01275469. ISSN 1432-0665. S2CID 35012853.
Friedman, H., Jensen, R. (1968). Note on admissible ordinals. In: Barwise, J. (eds) The Syntax and Semantics of Infinitary Languages. Lecture Notes in Mathematics, vol 72. Springer, Berlin, Heidelberg.
Sacks, Gerald E. (1976). "Countable admissible ordinals and hyperdegrees". Advances in Mathematics. 20 (2): 213–262. doi:10.1016/0001-8708(76)90187-0.
Richter, Wayne; Aczel, Peter (1974-01-01). "Inductive Definitions and Reflecting Properties of Admissible Ordinals" (PDF). Studies in Logic and the Foundations of Mathematics. 79: 301–381. doi:10.1016/S0049-237X(08)70592-5. hdl:10852/44063. ISBN 9780444105455. ISSN 0049-237X.
Simpson, Stephen G. (1978-01-01). "Short Course on Admissible Recursion Theory". Studies in Logic and the Foundations of Mathematics. 94: 355–390. doi:10.1016/S0049-237X(08)70941-8. ISBN 9780444851635. ISSN 0049-237X.

eudml.org

W. Marek, K. Rasmussen, Spectrum of L in libraries (WorldCat catalog) (EuDML page), Państwowe Wydawn. Accessed 2022-12-01.

handle.net

hdl.handle.net

Richter, Wayne; Aczel, Peter (1974-01-01). "Inductive Definitions and Reflecting Properties of Admissible Ordinals" (PDF). Studies in Logic and the Foundations of Mathematics. 79: 301–381. doi:10.1016/S0049-237X(08)70592-5. hdl:10852/44063. ISBN 9780444105455. ISSN 0049-237X.

leeds.ac.uk

www1.maths.leeds.ac.uk

"Ordinal notations based on a weakly Mahlo cardinal" (PDF). University of Leeds. 1990. Retrieved 2021-08-10.
"Proof Theory of Reflection" (PDF). University of Leeds. 1993-02-21. Retrieved 2021-08-10.

madore.org

"A Zoo of Ordinals" (PDF). Madore. 2017-07-29. Retrieved 2021-08-10.

psu.edu

personal.psu.edu

"Subsystems of Second-Order Arithmetic" (PDF). Penn State Institution. 2006-02-07. Retrieved 2010-08-10.

citeseerx.ist.psu.edu

F. G. Abramson, G. E. Sacks, "Uncountable Gandy Ordinals" (1976), p.387. Accessed 13 February 2023.

sciencedirect.com

W. Buchholz, "An independence result for $(\Pi _{1}^{1}{\mathsf {-CA}}){\mathsf {+BI}}$ . (1987)"
W. Buchholz, A new system of proof-theoretic ordinal functions (1984) (lemmata 1.3 and 1.8). Accessed 2022-05-04.
Simpson, Stephen G. (1978-01-01). "Short Course on Admissible Recursion Theory". Studies in Logic and the Foundations of Mathematics. 94: 355–390. doi:10.1016/S0049-237X(08)70941-8. ISBN 9780444851635. ISSN 0049-237X.
W. Chan, The countable admissible ordinal equivalence relation (2017), p.1233. Accessed 28 December 2022.

semanticscholar.org

api.semanticscholar.org

Rathjen, Michael (1994-01-01). "Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM". Archive for Mathematical Logic. 33 (1): 35–55. doi:10.1007/BF01275469. ISSN 1432-0665. S2CID 35012853.

stanford.edu

math.stanford.edu

S. Feferman, "Indescribable Cardinals and Admissible Analogues" (2013, unpublished). Accessed 18 November 2022.

uio.no

duo.uio.no

W. Richter, P. Aczel, Inductive Definitions and Reflection Properties of Admissible Ordinals (1973)
Richter, Wayne; Aczel, Peter (1974-01-01). "Inductive Definitions and Reflecting Properties of Admissible Ordinals" (PDF). Studies in Logic and the Foundations of Mathematics. 79: 301–381. doi:10.1016/S0049-237X(08)70592-5. hdl:10852/44063. ISBN 9780444105455. ISSN 0049-237X.

uni-muenster.de

miami.uni-muenster.de

Stegert, Jan-Carl (2010). "Ordinal proof theory of Kripke-Platek set theory augmented by strong reflection principles". miami.uni-muenster.de. Retrieved 2021-08-10.

worldcat.org

search.worldcat.org

Buchholz, W. (1986-01-01). "A new system of proof-theoretic ordinal functions". Annals of Pure and Applied Logic. 32: 195–207. doi:10.1016/0168-0072(86)90052-7. ISSN 0168-0072.
Rathjen, Michael (1994-01-01). "Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM". Archive for Mathematical Logic. 33 (1): 35–55. doi:10.1007/BF01275469. ISSN 1432-0665. S2CID 35012853.
Richter, Wayne; Aczel, Peter (1974-01-01). "Inductive Definitions and Reflecting Properties of Admissible Ordinals" (PDF). Studies in Logic and the Foundations of Mathematics. 79: 301–381. doi:10.1016/S0049-237X(08)70592-5. hdl:10852/44063. ISBN 9780444105455. ISSN 0049-237X.
Simpson, Stephen G. (1978-01-01). "Short Course on Admissible Recursion Theory". Studies in Logic and the Foundations of Mathematics. 94: 355–390. doi:10.1016/S0049-237X(08)70941-8. ISBN 9780444851635. ISSN 0049-237X.

worldcat.org

W. Marek, K. Rasmussen, Spectrum of L in libraries (WorldCat catalog) (EuDML page), Państwowe Wydawn. Accessed 2022-12-01.