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Axiom of regularity
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==Sources== * {{cite journal |first=Paul Isaac|last= Bernays|author-link=Paul Bernays| title= A system of axiomatic set theory. Part II |journal= The Journal of Symbolic Logic| volume= 6 |issue= 1| year = 1941 | pages = 1–17 | doi=10.2307/2267281 | jstor=2267281|s2cid= 250344277}} * {{cite journal | first= Paul Isaac|last = Bernays|author-link=Paul Bernays| title= A system of axiomatic set theory. Part VII |journal = The Journal of Symbolic Logic| volume = 19 |issue = 2| year = 1954 | pages = 81–96 | doi=10.2307/2268864 | jstor=2268864| s2cid=250351655 | url = http://doc.rero.ch/record/301843/files/S0022481200087570.pdf}} *{{cite journal|last=Boolos|first= George |author-link=George Boolos | year= 1971 | title = The iterative conception of set | journal = Journal of Philosophy | volume = 68 |issue= 8 |pages= 215–231 | doi=10.2307/2025204 | jstor=2025204}} Reprinted in {{cite book|last=Boolos|first= George |year=1998|title=Logic, Logic and Logic|pages=13–29|publisher=Harvard University Press}} *{{cite book | last= Enderton | first = Herbert B. | title = Elements of Set Theory | publisher = Academic Press | year=1977}} *{{cite book|title = Logic, induction and sets| last = Forster | first = T. | publisher = Cambridge University Press | year = 2003}} *{{cite book| first= Lorenz J. |last = Halbeisen | title=Combinatorial Set Theory: With a Gentle Introduction to Forcing|year=2012|publisher=Springer}} * {{cite book|first=Michael|last=Hallett|title=Cantorian set theory and limitation of size|publisher=Oxford University Press|year=1996|orig-year=first published 1984|isbn=978-0-19-853283-5}} *{{cite book | last=Jech | first= Thomas |author-link=Thomas Jech | year= 2003 |title = Set Theory |edition=Third Millennium |publisher=Springer| isbn = 978-3-540-44085-7}} *{{cite book | last=Kunen | first=Kenneth |author-link=Kenneth Kunen | year = 1980|title = Set Theory: An Introduction to Independence Proofs| publisher=Elsevier| isbn=978-0-444-86839-8}} *{{cite book| last = Lévy | first =Azriel | author-link=Azriel Lévy | isbn = 978-0-486-42079-0 | year =2002 |orig-year= first published in 1979 | title=Basic set theory| publisher=Dover Publications|location=Mineola, New York}} *{{cite journal | last1=Mirimanoff | first1=Dmitry |author-link=Dmitry Mirimanoff| title=Les antinomies de Russell et de Burali-Forti et le probleme fondamental de la theorie des ensembles |language=fr | year=1917 | journal=L'Enseignement Mathématique | volume=19|pages=37–52}} *{{cite book|editor1-first=Godehard |editor1-last=Link|title=One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy|year=2004|publisher=Walter de Gruyter|isbn=978-3-11-019968-0| chapter =Predicativity, Circularity, and Anti-Foundation | first = M. | last= Rathjen| chapter-url=http://www1.maths.leeds.ac.uk/~rathjen/russelle.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www1.maths.leeds.ac.uk/~rathjen/russelle.pdf |archive-date=2022-10-09 |url-status=live}} * {{cite book | last1 = Rieger | first1 = Adam | chapter = Paradox, ZF, and the Axiom of Foundation | doi = 10.1007/978-94-007-0214-1_9 | title = Logic, Mathematics, Philosophy, Vintage Enthusiasms. Essays in Honour of John L. Bell | editor-last1= DeVidi|editor-first1=David|editor-last2=Hallett|editor-first2=Michael|editor-last3=Clark|editor-first3=Peter | series = The Western Ontario Series in Philosophy of Science | volume = 75 | pages = 171–187 | year = 2011 | isbn = 978-94-007-0213-4 | chapter-url = http://eprints.gla.ac.uk/3810/1/JLB.pdf| citeseerx = 10.1.1.100.9052 }} * {{cite journal | first = L. |last = Riegger | url = http://dml.cz/bitstream/handle/10338.dmlcz/100254/CzechMathJ_07-1957-3_1.pdf | title = A contribution to Gödel's axiomatic set theory | journal = Czechoslovak Mathematical Journal | volume = 7 | year = 1957 |issue = 3 | pages = 323–357|doi = 10.21136/CMJ.1957.100254 | doi-access = free }} *{{cite book| first = Davide | last = Sangiorgi | year = 2011 | chapter = Origins of bisimulation and coinduction | editor1-first = Davide | editor1-last = Sangiorgi | editor2-first = Jan | editor2-last = Rutten | title = Advanced Topics in Bisimulation and Coinduction | publisher = Cambridge University Press}} * {{cite book | last = Scott | first = Dana Stewart | author-link=Dana Scott | year = 1974 | chapter = Axiomatizing set theory | title = Axiomatic set theory. Proceedings of Symposia in Pure Mathematics |volume=13 |at=Part II, pp. 207–214}} * {{cite book | last=Skolem| first=Thoralf|author-link=Thoralf Skolem | year=1923|title=Axiomatized set theory}} Reprinted in ''From Frege to Gödel'', van Heijenoort, 1967, in English translation by Stefan Bauer-Mengelberg, pp. 291–301. * {{cite book|first=Patrick|last=Suppes|author-link=Patrick Suppes|title=Axiomatic Set Theory|publisher=Dover |year=1972|orig-year=first published 1960|isbn=978-0-486-61630-8}} *{{cite book|last = Urquhart|first = Alasdair | chapter = The Theory of Types | editor-last = Griffin| editor-first =Nicholas | title =The Cambridge Companion to Bertrand Russell | publisher = Cambridge University Press | year=2003}} * {{cite book|first=Robert L. |last = Vaught|title=Set Theory: An Introduction| year=2001| publisher=Springer| isbn=978-0-8176-4256-3| edition=2nd}} *{{cite journal|last=von Neumann|first = John| author-link=John von Neumann|year=1925|title=Eine Axiomatisierung der Mengenlehre|language=de|journal=Journal für die Reine und Angewandte Mathematik|volume=154|pages=219–240}} Translation in {{cite book|last=van Heijenoort | first =Jean | year =1967 | title = From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 | pages = 393–413 }} *{{cite journal|last = von Neumann|first = John| author-link=John von Neumann |year= 1928|title= Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre|language=de| journal= Mathematische Annalen|volume = 99 |pages=373–391|doi=10.1007/BF01459102|s2cid = 120784562}} *{{cite journal| last = von Neumann |first = John| author-link=John von Neumann| year = 1929 | title= Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre|language=de| journal = Journal für die Reine und Angewandte Mathematik |volume = 1929 |issue = 160|pages = 227–241 | doi=10.1515/crll.1929.160.227|s2cid = 199545822}} *{{cite journal |last=Zermelo|first= Ernst |author-link=Ernst Zermelo | year= 1930 | title = Über Grenzzahlen und Mengenbereiche. Neue Untersuchungen über die Grundlagen der Mengenlehre |language=de| journal = Fundamenta Mathematicae | volume = 16 |pages= 29–47|url=http://matwbn.icm.edu.pl/ksiazki/fm/fm16/fm1615.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://matwbn.icm.edu.pl/ksiazki/fm/fm16/fm1615.pdf |archive-date=2022-10-09 |url-status=live|doi= 10.4064/fm-16-1-29-47 |doi-access= free }} Translation in {{cite book | editor-last= Ewald |editor-first= W. B. | year = 1996| title = From Kant to Hilbert: A Source Book in the Foundations of Mathematics |volume=2 | publisher= Clarendon Press |pages = 1219–1233}}
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