Tiên đề chọn (Vietnamese Wikipedia)

Analysis of information sources in references of the Wikipedia article "Tiên đề chọn" in Vietnamese language version.

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8doi.org

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6archive.org

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3books.google.com

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2uni-goettingen.de

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2harvard.edu

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2nih.gov

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1zbmath.org

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1cmu.edu

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1stanford.edu

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ams.org

Fraenkel, Abraham A.; Bar-Hillel, Yehoshua; Lévy, Azriel (1973), Foundations of set theory (ấn bản 2), Amsterdam-London: North-Holland Publishing Co., tr. 69–70, ISBN 9780080887050, MR 0345816.
Blass, Andreas (1984). “Existence of bases implies the axiom of choice”. Axiomatic set theory (Boulder, Colo., 1983). Contemporary Mathematics. 31. Providence, RI: American Mathematical Society. tr. 31–33. doi:10.1090/conm/031/763890. MR 0763890.
Serre, Jean-Pierre (2003), Trees, Springer Monographs in Mathematics, Springer, tr. 23; Soukup, Lajos (2008), “Infinite combinatorics: from finite to infinite”, Horizons of combinatorics, Bolyai Society Mathematical Studies, 17, Berlin: Springer, tr. 189–213, CiteSeerX 10.1.1.222.5699, doi:10.1007/978-3-540-77200-2_10, ISBN 978-3-540-77199-9, MR 2432534. Định lý 2.1, pp. 192–193.

archive.org

Jech, 1977, p. 348ff; Martin-Löf 2008, p. 210. Theo Mendelson 1964, tr. 201:
The status of the Axiom of Choice has become less controversial in recent years. To most mathematicians it seems quite plausible and it has so many important applications in practically all branches of mathematics that not to accept it would seem to be a wilful hobbling of the practicing mathematician.
Mendelson, Elliott (1964). Introduction to Mathematical Logic. New York: Van Nostrand Reinhold.
Herrlich 2006, tr. 9. Theo Suppes 1972, tr. 243, phát biểu này do Zermelo 1904 đưa ra. Xem thêm Halmos 1960, tr. 60. Herrlich, Horst (2006). Axiom of Choice. Lecture Notes in Math. 1876. Berlin: Springer-Verlag. ISBN 978-3-540-30989-5. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935. Halmos, Paul R. (1960). Naive Set Theory. The University Series in Undergraduate Mathematics. Princeton, NJ: van Nostrand Company. Zbl 0087.04403.
Suppes 1972, tr. 240. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8.
Martin-Löf, Per (2006). “100 Years of Zermelo's Axiom of Choice: What was the Problem with It?”. The Computer Journal. 49 (3): 345–350. Bibcode:1980CompJ..23..262L. doi:10.1093/comjnl/bxh162.
Xem Moore 2013, tr. 330–334, danh sách 74 mệnh đề tương đương. Xem Howard & Rubin 1998, tr. 11–16, danh sách 86 mệnh đề tương đương với nguồn tham khảo. Moore, Gregory H (2013) [1982]. Zermelo's axiom of choice: Its origins, development & influence. Mineola, New York: Dover Publications. ISBN 978-0-486-48841-7. Howard, Paul; Rubin, Jean E. (1998). Consequences of the axiom of choice. Mathematical Surveys and Monographs. 59. Providence, Rhode Island: American Mathematical Society. ISBN 9780821809778.
Awodey, Steve (2010). Category theory (ấn bản 2). Oxford: Oxford University Press. tr. 20–24. ISBN 978-0199237180. OCLC 740446073.

books.google.com

Fraenkel, Abraham A.; Bar-Hillel, Yehoshua; Lévy, Azriel (1973), Foundations of set theory (ấn bản 2), Amsterdam-London: North-Holland Publishing Co., tr. 69–70, ISBN 9780080887050, MR 0345816.
Rosenbloom, Paul C. (2005), The Elements of Mathematical Logic, Courier Dover Publications, tr. 147, ISBN 9780486446172.
Serre, Jean-Pierre (2003), Trees, Springer Monographs in Mathematics, Springer, tr. 23; Soukup, Lajos (2008), “Infinite combinatorics: from finite to infinite”, Horizons of combinatorics, Bolyai Society Mathematical Studies, 17, Berlin: Springer, tr. 189–213, CiteSeerX 10.1.1.222.5699, doi:10.1007/978-3-540-77200-2_10, ISBN 978-3-540-77199-9, MR 2432534. Định lý 2.1, pp. 192–193.

cmu.edu

cs.cmu.edu

Per Martin-Löf, Intuitionistic type theory, 1980. Anne Sjerp Troelstra, Metamathematical investigation of intuitionistic arithmetic and analysis, Springer, 1973.

doi.org

Zermelo 1904. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935.
Herrlich 2006, tr. 9. Theo Suppes 1972, tr. 243, phát biểu này do Zermelo 1904 đưa ra. Xem thêm Halmos 1960, tr. 60. Herrlich, Horst (2006). Axiom of Choice. Lecture Notes in Math. 1876. Berlin: Springer-Verlag. ISBN 978-3-540-30989-5. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935. Halmos, Paul R. (1960). Naive Set Theory. The University Series in Undergraduate Mathematics. Princeton, NJ: van Nostrand Company. Zbl 0087.04403.
Dawson, J. W. (tháng 8 năm 2006), “Shaken Foundations or Groundbreaking Realignment? A Centennial Assessment of Kurt Gödel's Impact on Logic, Mathematics, and Computer Science”, Proc. 21st Annual IEEE Symposium on Logic in Computer Science (LICS 2006), tr. 339–341, doi:10.1109/LICS.2006.47, ISBN 978-0-7695-2631-7, S2CID 15526447, The axiom of choice, though it had been employed unconsciously in many arguments in analysis, became controversial once made explicit, not only because of its non-constructive character, but because it implied such extremely unintuitive consequences as the Banach–Tarski paradox.
Martin-Löf, Per (2006). “100 Years of Zermelo's Axiom of Choice: What was the Problem with It?”. The Computer Journal. 49 (3): 345–350. Bibcode:1980CompJ..23..262L. doi:10.1093/comjnl/bxh162.
Richman, Fred (2001). “Constructive Mathematics without Choice”. Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Dordrecht: Springer Netherlands. tr. 199–205. doi:10.1007/978-94-015-9757-9_17.
Gödel, Kurt (ngày 9 tháng 11 năm 1938). “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis”. Proceedings of the National Academy of Sciences of the United States of America. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.
Blass, Andreas (1984). “Existence of bases implies the axiom of choice”. Axiomatic set theory (Boulder, Colo., 1983). Contemporary Mathematics. 31. Providence, RI: American Mathematical Society. tr. 31–33. doi:10.1090/conm/031/763890. MR 0763890.
Serre, Jean-Pierre (2003), Trees, Springer Monographs in Mathematics, Springer, tr. 23; Soukup, Lajos (2008), “Infinite combinatorics: from finite to infinite”, Horizons of combinatorics, Bolyai Society Mathematical Studies, 17, Berlin: Springer, tr. 189–213, CiteSeerX 10.1.1.222.5699, doi:10.1007/978-3-540-77200-2_10, ISBN 978-3-540-77199-9, MR 2432534. Định lý 2.1, pp. 192–193.

harvard.edu

ui.adsabs.harvard.edu

Martin-Löf, Per (2006). “100 Years of Zermelo's Axiom of Choice: What was the Problem with It?”. The Computer Journal. 49 (3): 345–350. Bibcode:1980CompJ..23..262L. doi:10.1093/comjnl/bxh162.
Gödel, Kurt (ngày 9 tháng 11 năm 1938). “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis”. Proceedings of the National Academy of Sciences of the United States of America. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.

ncatlab.org

projective object tại nLab

nih.gov

ncbi.nlm.nih.gov

Gödel, Kurt (ngày 9 tháng 11 năm 1938). “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis”. Proceedings of the National Academy of Sciences of the United States of America. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.

pubmed.ncbi.nlm.nih.gov

Gödel, Kurt (ngày 9 tháng 11 năm 1938). “The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis”. Proceedings of the National Academy of Sciences of the United States of America. 24 (12): 556–557. Bibcode:1938PNAS...24..556G. doi:10.1073/pnas.24.12.556. PMC 1077160. PMID 16577857.

psu.edu

citeseerx.ist.psu.edu

Serre, Jean-Pierre (2003), Trees, Springer Monographs in Mathematics, Springer, tr. 23; Soukup, Lajos (2008), “Infinite combinatorics: from finite to infinite”, Horizons of combinatorics, Bolyai Society Mathematical Studies, 17, Berlin: Springer, tr. 189–213, CiteSeerX 10.1.1.222.5699, doi:10.1007/978-3-540-77200-2_10, ISBN 978-3-540-77199-9, MR 2432534. Định lý 2.1, pp. 192–193.

semanticscholar.org

api.semanticscholar.org

Zermelo 1904. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935.
Herrlich 2006, tr. 9. Theo Suppes 1972, tr. 243, phát biểu này do Zermelo 1904 đưa ra. Xem thêm Halmos 1960, tr. 60. Herrlich, Horst (2006). Axiom of Choice. Lecture Notes in Math. 1876. Berlin: Springer-Verlag. ISBN 978-3-540-30989-5. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935. Halmos, Paul R. (1960). Naive Set Theory. The University Series in Undergraduate Mathematics. Princeton, NJ: van Nostrand Company. Zbl 0087.04403.
Dawson, J. W. (tháng 8 năm 2006), “Shaken Foundations or Groundbreaking Realignment? A Centennial Assessment of Kurt Gödel's Impact on Logic, Mathematics, and Computer Science”, Proc. 21st Annual IEEE Symposium on Logic in Computer Science (LICS 2006), tr. 339–341, doi:10.1109/LICS.2006.47, ISBN 978-0-7695-2631-7, S2CID 15526447, The axiom of choice, though it had been employed unconsciously in many arguments in analysis, became controversial once made explicit, not only because of its non-constructive character, but because it implied such extremely unintuitive consequences as the Banach–Tarski paradox.

stanford.edu

stacks.stanford.edu

Cohen, Paul (2019). “The Independence of the Axiom of Choice” (PDF). Stanford University Libraries. Truy cập ngày 22 tháng 3 năm 2019.

uni-goettingen.de

gdz.sub.uni-goettingen.de

Zermelo 1904. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935.
Herrlich 2006, tr. 9. Theo Suppes 1972, tr. 243, phát biểu này do Zermelo 1904 đưa ra. Xem thêm Halmos 1960, tr. 60. Herrlich, Horst (2006). Axiom of Choice. Lecture Notes in Math. 1876. Berlin: Springer-Verlag. ISBN 978-3-540-30989-5. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935. Halmos, Paul R. (1960). Naive Set Theory. The University Series in Undergraduate Mathematics. Princeton, NJ: van Nostrand Company. Zbl 0087.04403.

worldcat.org

Awodey, Steve (2010). Category theory (ấn bản 2). Oxford: Oxford University Press. tr. 20–24. ISBN 978-0199237180. OCLC 740446073.

zbmath.org

Herrlich 2006, tr. 9. Theo Suppes 1972, tr. 243, phát biểu này do Zermelo 1904 đưa ra. Xem thêm Halmos 1960, tr. 60. Herrlich, Horst (2006). Axiom of Choice. Lecture Notes in Math. 1876. Berlin: Springer-Verlag. ISBN 978-3-540-30989-5. Suppes, Patrick (1972) [1960]. Axiomatic set theory. Mineola, New York: Dover. ISBN 978-0-486-61630-8. Zermelo, Ernst (1904). “Beweis, dass jede Menge wohlgeordnet werden kann” (reprint). Mathematische Annalen. 59 (4): 514–16. doi:10.1007/BF01445300. S2CID 124189935. Halmos, Paul R. (1960). Naive Set Theory. The University Series in Undergraduate Mathematics. Princeton, NJ: van Nostrand Company. Zbl 0087.04403.