Axiom of regularity (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Axiom of regularity" in English language version.

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7doi.org

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3ghostarchive.org

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2icm.edu.pl

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2semanticscholar.org

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2arxiv.org

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2gla.ac.uk

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2psu.edu

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1leeds.ac.uk

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1jstor.org

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arxiv.org

Shulman, Michael (2018). "Comparing material and structural set theories". Annals of Pure and Applied Logic. 170 (4): 465–504. arXiv:1808.05204. doi:10.1016/j.apal.2018.11.002.
Pinsky, Brian (2023). "Frucht's Theorem without Choice". arXiv:2305.11382 [math.LO].

doi.org

Zermelo 1930. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233.
von Neumann 1929. von Neumann, John (1929). "Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre". Journal für die Reine und Angewandte Mathematik (in German). 1929 (160): 227–241. doi:10.1515/crll.1929.160.227. S2CID 199545822.
Shulman, Michael (2018). "Comparing material and structural set theories". Annals of Pure and Applied Logic. 170 (4): 465–504. arXiv:1808.05204. doi:10.1016/j.apal.2018.11.002.
Rieger 2011, pp. 175, 178. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.
The details of this implicit typing are spelled out in Zermelo 1930, and again in Boolos 1971. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233. Boolos, George (1971). "The iterative conception of set". Journal of Philosophy. 68 (8): 215–231. doi:10.2307/2025204. JSTOR 2025204. Reprinted in Boolos, George (1998). Logic, Logic and Logic. Harvard University Press. pp. 13–29.
Rieger 2011, p. 179. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.
von Neumann 1929, p. 231. von Neumann, John (1929). "Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre". Journal für die Reine und Angewandte Mathematik (in German). 1929 (160): 227–241. doi:10.1515/crll.1929.160.227. S2CID 199545822.

ghostarchive.org

Zermelo 1930. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233.
Rathjen 2004, p. 193. Rathjen, M. (2004). "Predicativity, Circularity, and Anti-Foundation" (PDF). In Link, Godehard (ed.). One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy. Walter de Gruyter. ISBN 978-3-11-019968-0. Archived (PDF) from the original on 2022-10-09.
The details of this implicit typing are spelled out in Zermelo 1930, and again in Boolos 1971. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233. Boolos, George (1971). "The iterative conception of set". Journal of Philosophy. 68 (8): 215–231. doi:10.2307/2025204. JSTOR 2025204. Reprinted in Boolos, George (1998). Logic, Logic and Logic. Harvard University Press. pp. 13–29.

gla.ac.uk

eprints.gla.ac.uk

Rieger 2011, pp. 175, 178. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.
Rieger 2011, p. 179. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.

icm.edu.pl

matwbn.icm.edu.pl

Zermelo 1930. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233.
The details of this implicit typing are spelled out in Zermelo 1930, and again in Boolos 1971. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233. Boolos, George (1971). "The iterative conception of set". Journal of Philosophy. 68 (8): 215–231. doi:10.2307/2025204. JSTOR 2025204. Reprinted in Boolos, George (1998). Logic, Logic and Logic. Harvard University Press. pp. 13–29.

jstor.org

The details of this implicit typing are spelled out in Zermelo 1930, and again in Boolos 1971. Zermelo, Ernst (1930). "Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre" (PDF). Fundamenta Mathematicae (in German). 16: 29–47. doi:10.4064/fm-16-1-29-47. Archived (PDF) from the original on 2022-10-09. Translation in Ewald, W. B., ed. (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. 2. Clarendon Press. pp. 1219–1233. Boolos, George (1971). "The iterative conception of set". Journal of Philosophy. 68 (8): 215–231. doi:10.2307/2025204. JSTOR 2025204. Reprinted in Boolos, George (1998). Logic, Logic and Logic. Harvard University Press. pp. 13–29.

leeds.ac.uk

www1.maths.leeds.ac.uk

Rathjen 2004, p. 193. Rathjen, M. (2004). "Predicativity, Circularity, and Anti-Foundation" (PDF). In Link, Godehard (ed.). One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy. Walter de Gruyter. ISBN 978-3-11-019968-0. Archived (PDF) from the original on 2022-10-09.

psu.edu

citeseerx.ist.psu.edu

Rieger 2011, pp. 175, 178. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.
Rieger 2011, p. 179. Rieger, Adam (2011). "Paradox, ZF, and the Axiom of Foundation" (PDF). In DeVidi, David; Hallett, Michael; Clark, Peter (eds.). Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell. The Western Ontario Series in Philosophy of Science. Vol. 75. pp. 171–187. CiteSeerX 10.1.1.100.9052. doi:10.1007/978-94-007-0214-1_9. ISBN 978-94-007-0213-4.

semanticscholar.org

api.semanticscholar.org

von Neumann 1929. von Neumann, John (1929). "Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre". Journal für die Reine und Angewandte Mathematik (in German). 1929 (160): 227–241. doi:10.1515/crll.1929.160.227. S2CID 199545822.
von Neumann 1929, p. 231. von Neumann, John (1929). "Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre". Journal für die Reine und Angewandte Mathematik (in German). 1929 (160): 227–241. doi:10.1515/crll.1929.160.227. S2CID 199545822.