Reverse mathematics (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Reverse mathematics" in English language version.

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Harvey Friedman (1975, 1976) Friedman, Harvey (1975), "Some systems of second-order arithmetic and their use", Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Montreal: Canad. Math. Congress, pp. 235–242, MR 0429508 Friedman, Harvey (1976), Baldwin, John; Martin, D. A.; Soare, R. I.; Tait, W. W. (eds.), "Systems of second-order arithmetic with restricted induction, I, II", Meeting of the Association for Symbolic Logic, The Journal of Symbolic Logic, 41 (2): 557–559, doi:10.2307/2272259, JSTOR 2272259
Simpson (2009). Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p.42. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p. 6. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Schmerl, James H. (2000). "Graph coloring and reverse mathematics". Mathematical Logic Quarterly. 46 (4): 543–548. doi:10.1002/1521-3870(200010)46:4<543::AID-MALQ543>3.0.CO;2-E. MR 1791549.

arxiv.org

Normann & Sanders (2018). Normann, Dag; Sanders, Sam (2018), "On the mathematical and foundational significance of the uncountable", Journal of Mathematical Logic, 19: 1950001, arXiv:1711.08939, doi:10.1142/S0219061319500016, S2CID 119120366
Kołodziejczyk, Leszek; Michalewski, Henryk (2016). How unprovable is Rabin's decidability theorem?. LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. arXiv:1508.06780.

brics.dk

Kohlenbach (2005). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846
See Kohlenbach (2005) and Hunter (2008). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846 Hunter, James (2008), Reverse Topology (PDF) (PhD thesis), University of Wisconsin–Madison

core.ac.uk

S. Takashi, "Reverse Mathematics and Countable Algebraic Systems". Ph.D. thesis, Tohoku University, 2016.

doi.org

Harvey Friedman (1975, 1976) Friedman, Harvey (1975), "Some systems of second-order arithmetic and their use", Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Montreal: Canad. Math. Congress, pp. 235–242, MR 0429508 Friedman, Harvey (1976), Baldwin, John; Martin, D. A.; Soare, R. I.; Tait, W. W. (eds.), "Systems of second-order arithmetic with restricted induction, I, II", Meeting of the Association for Symbolic Logic, The Journal of Symbolic Logic, 41 (2): 557–559, doi:10.2307/2272259, JSTOR 2272259
Kohlenbach (2005). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846
See Kohlenbach (2005) and Hunter (2008). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846 Hunter, James (2008), Reverse Topology (PDF) (PhD thesis), University of Wisconsin–Madison
Normann & Sanders (2018). Normann, Dag; Sanders, Sam (2018), "On the mathematical and foundational significance of the uncountable", Journal of Mathematical Logic, 19: 1950001, arXiv:1711.08939, doi:10.1142/S0219061319500016, S2CID 119120366
Simpson (2009). Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p.42. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p. 6. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Schmerl, James H. (2000). "Graph coloring and reverse mathematics". Mathematical Logic Quarterly. 46 (4): 543–548. doi:10.1002/1521-3870(200010)46:4<543::AID-MALQ543>3.0.CO;2-E. MR 1791549.
Montalban, Antonio; Shore, Richard (2014). "The limits of determinacy in second order arithmetic: consistency and complexity strength". Israel Journal of Mathematics. 204: 477–508. doi:10.1007/s11856-014-1117-9. S2CID 287519.

jstor.org

Harvey Friedman (1975, 1976) Friedman, Harvey (1975), "Some systems of second-order arithmetic and their use", Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Montreal: Canad. Math. Congress, pp. 235–242, MR 0429508 Friedman, Harvey (1976), Baldwin, John; Martin, D. A.; Soare, R. I.; Tait, W. W. (eds.), "Systems of second-order arithmetic with restricted induction, I, II", Meeting of the Association for Symbolic Logic, The Journal of Symbolic Logic, 41 (2): 557–559, doi:10.2307/2272259, JSTOR 2272259

kyoto-u.ac.jp

repository.kulib.kyoto-u.ac.jp

M. Fujiwara, T. Sato, "Note on total and partial functions in second-order arithmetic". In 1950 Proof Theory, Computation Theory and Related Topics, June 2015.

nyu.edu

cs.nyu.edu

Kołodziejczyk, Leszek (October 19, 2015). "Question on Decidability of S2S". FOM.

psu.edu

math.psu.edu

Simpson (2009). Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p.42. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689
Simpson (2009), p. 6. Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978-0-521-88439-6, MR 2517689

citeseerx.ist.psu.edu

Kohlenbach (2005). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846
See Kohlenbach (2005) and Hunter (2008). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846 Hunter, James (2008), Reverse Topology (PDF) (PhD thesis), University of Wisconsin–Madison

semanticscholar.org

api.semanticscholar.org

Normann & Sanders (2018). Normann, Dag; Sanders, Sam (2018), "On the mathematical and foundational significance of the uncountable", Journal of Mathematical Logic, 19: 1950001, arXiv:1711.08939, doi:10.1142/S0219061319500016, S2CID 119120366
Montalban, Antonio; Shore, Richard (2014). "The limits of determinacy in second order arithmetic: consistency and complexity strength". Israel Journal of Mathematics. 204: 477–508. doi:10.1007/s11856-014-1117-9. S2CID 287519.

tu-darmstadt.de

www2.mathematik.tu-darmstadt.de

Kohlenbach (2005). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846
See Kohlenbach (2005) and Hunter (2008). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846 Hunter, James (2008), Reverse Topology (PDF) (PhD thesis), University of Wisconsin–Madison

wisc.edu

math.wisc.edu

See Kohlenbach (2005) and Hunter (2008). Kohlenbach, Ulrich (2005), "Higher order reverse mathematics", in Simpson, Stephen G (ed.), Higher Order Reverse Mathematics, Reverse Mathematics 2001 (PDF), Lecture notes in Logic, Cambridge University Press, pp. 281–295, CiteSeerX 10.1.1.643.551, doi:10.1017/9781316755846.018, ISBN 9781316755846 Hunter, James (2008), Reverse Topology (PDF) (PhD thesis), University of Wisconsin–Madison

youtube.com

Simpson claims to have not invented the term. [Simpson, S.; Eastaugh, B.; Dean, W. (June 17, 2022). "Panel Discussion". YouTube. Paris, France: University of Chicago, Reverse Mathematics and its Philosophy.]