Bibliography - Mathematics

MATH 800 FOUNDATIONS OF MATHEMATICS JT SMITH
BIBLIOGRAPHY SPRING 2008
I’ll accumulate in this file detailed references to all items that I cite during this course.
Thus, its content will change often and without notice. I’m using the style that I adopted
for the Marchisotto and Smith 2007 bibliography, which in turn is patterned on the
documentation two style of Chicago 1993. Alphabetization of the entries ignores diacritical
marks, punctuation, and spaces within names.
Some cited works have appeared in several editions. Information about the first often
has historical interest, even when reference to a later one is more appropriate. In such
cases, both dates are given, as in “Stoll, Robert J. [1963] 1979.” The remaining data in
such citations refer to the later edition unless otherwise specified. Book citations often
include an International Standard Book Number (ISBN) and a Library of Congress (LC)
1 2
catalog number. Some cited publications are now available on the Internet, but no
standard means of locating them has yet evolved. Notations such as “Internet: AMS”
are provided to help you locate publications in academic Internet repositories. The
notation after the colon (:) identifies an Internet http:// address in the following list:
1
Caution! A book may have similar editions with different ISBNs. Moreover, the LC number is not
standard, unless the book was cataloged upon publication and its number included on the copyright page.
From one library to the next, the LC number may vary slightly— particularly its last digits.
2
AMS............. www.ams.org
Bielefeld. . . . . . . . . dml.math.uni-bielefeld.de/JB_DMV/
Euclid. . . . . . . . . . . projecteuclid.org
Göttingen. . . . . . . . gdz.sub.uni-goettingen.de
JSTOR.. . . . . . . . . . www.jstor.org
NUMDAM.. . . . . . . archive.numdam.org
Poland. . . . . . . . . . . matwbn.icm.edu.pl
Springer. . . . . . . . . springerlink.metapress.com
The citations contain brief annotations that explain their origin, import, or relationship
to other items. Each annotation concludes with a list [in brackets] of the parts of
this course and other items in this bibliography that contain references to it. An annotation
may include a code in the format “MSN: reviewer” or “JSL m(date): n reviewer”
to indicate that it was reviewed on MathSciNet or in the Journal of Symbolic Logic,
volume m, page n. The standard sources of reviews for publications in foundations of
mathematics, these are available via Internet: AMS and Internet: JSTOR. Students can
sometimes gain important insights and an overview quickly from reviews.
Many Internet sources are free, but some— for example JSTOR — are free only through libraries— for
example, ours— with paid subscriptions, or through individual subscriptions.
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Page 2 MATH 800 BIBLIOGRAPHY SPRING 2008
Baire, René, Emile Borel, Jacques Hadamard, and Henri Lebesgue. [1905] 1982. Five letters
on set theory. Translated by Gregory H. Moore. In Moore [1982], Appendix I, 311–320.
Originally published as “Cinq lettres sur la théorie des ensembles,” Bulletin de la Société
Mathématique de France 33: 261–273. LC: QA1.S63. Internet: NUMDAM. [Cited in the Maximal
Principles unit.]
Banach, Stefan. 1924. Un théorème sur les transformations biunivoques. Fundamenta Mathematicæ
6: 236–239. LC: QA1.F8. Internet: Poland. [Cited in outline 15.]
Bell, John L., and David H. Fremlin. 1972. The maximal ideal theorem for lattices of sets.
Bulletin of the London Mathematical Society 4: 1–2. LC: QA1.L58.B8. MSN: P. E. Howard.
[Cited in the Maximal Principles unit.]
Bernays, Paul. 1926. Axiomatische Untersuchungen des Aussagenkalküls der Principia Mathematica.
Mathematische Zeitschrift 25. LC: QA1.M3. Internet: Göttingen. This work was
completed in 1919. [Cited in outline 35.]
———. 1941. A system of axiomatic set theory, Part II. Journal of Symbolic Logic 6: 1–17. LC:
BC1.J6. Internet: JSTOR. MSN: H. B. Curry. JSL 3(1938): 49 W. V. O. Quine, 9(1944): 74–75
L. W. Loomis. [Cited in the Axiom of Choice unit.]
Bettazzi, Rodolfo. 1892. Sui punti di discontinuità delle funzioni di variabile reale. Rendiconti
del Circolo Matematico di Palermo 6: 173–195. LC: QA1.C52. [Cited in outline 17.]
———. 1896. Gruppi finiti ed infiniti di enti. Atti della Reale Accademia delle Scienze di Torino
31(1895–1896): 506–512. LC: AS222.A29. Continuation of 1896a. [Cited in outlines 17 and
23.]
Birkhoff, Garrett. 1937. An extended arithmetic. Duke Mathematical Journal 3: 311–316. LC:
QA1.D8. JSL 7(1942): 125–126 A. Church. [Cited in the Partially Ordered Sets unit.]
———. 1948. Lattice Theory. Colloquium publications, volume 25. Revised edition. Providence:
American Mathematical Society. LC: QA171.5.B5. MSN: O. Frink. The first edition was
published in 1940. See also the third edition, 1967. The editions differ considerably. JSL
5(1940): 155–157 H. E. Vaughn, 15(1950): A. Church. [Cited in the Equivalences and Partitions,
Partially Ordered Sets and Complete Lattices units and in outline 5.]
Borel, Émile. 1898. Leçons sur la théorie des fonctions. Paris: Gauthier–Villars. LC: QA331.B6.
[Cited in outline 12.]
Bourbaki, Nicolas. 1939. Éléments de mathématique. Part I: Les structures fondamentales de
l’analyse. Livre I: Théorie des ensembles (Fascicule de résultats). Actualités scientifiques et
industrielles, 846. Paris: Hermann & Cie. LC: QA37.B646. MSN: S. Eilenberg. [Cited in the
Maximal Principles unit.]
———. 1968. Theory of Sets. Elements of mathematics, part 1, book 1. Reading, Massachusetts:
Addison–Wesley. LC: QA248.B73413. MSN: Anonymous. JSL 40(1975): 630–631 P.
Smith. [Cited in the Basic Set Theory unit.]
Burali-Forti, Cesare. [1897] 1970. A question on transfinite numbers. Translated by Jean van
Heijenoort. In Heijenoort [1967] 1970, 104–111. Originally published as “Una questione sui
numeri transfiniti,” Rendiconti del Circolo Matematico di Palermo 11: 154–164, LC: QA1.C52.
[Cited in the Maximal Principles unit.]
Cantor, Georg. 1874 [1996]. On a property of the set of real algebraic numbers. Translated by
William Ewald. In Ewald 1996, volume 2, section 19.A, 839–843. Originally published as
“Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen,” Journal für die
reine und angewandte Mathematik 77: 258–262, LC: QA1.J6, Internet: Göttingen. [Cited in
the Cardinals II unit.]
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MATH 800 BIBLIOGRAPHY SPRING 2008 Page 3
———. 1878. Ein Beitrag zur Mannigfaltigkeitslehre. Journal für die reine und angewandte
Mathematik 84: 242–258. LC: QA1.J6. Internet: Göttingen. Reprinted in Cantor [1932] 1962,
119–133. [Cited in outlines 11, 12 and item Cantor [1932] 1962.]
———. 1879–1884. Über unendliche lineare Punktmannigfaltigkeiten. Mathematische Annalen
15(1879): 1–7; 17(1880): 355–358; 20(1882): 113–121; 21(1883): 51–58, 545– 586; 23(1884):
453–488. LC: QA1.M29. Internet: Göttingen. Reprinted in G. Cantor [1932] 1962, 139–
246. Cantor [1883] 1996 is a translation of its fifth part. [Cited in outline 17 and items
G. Cantor [1932] 1962, [1883] 1996.]
———. [1883] 1996. Foundations of a general theory of manifolds: A mathematico-philosophical
investigation into the theory of the infinite. Translated by William Ewald. In Ewald 1996,
volume 2, section 19.C, 878–920. The original book, published by B. G. Teubner, is a reprint,
with additional preface and footnotes, of the fifth part of G. Cantor 1879–1884. [Cited in item
Cantor 1879–1884.]
———. 1884. De la puissance des ensembles parfaits de points. Acta Mathematica 4: 381–392.
LC: QA1.A3. Internet: Springer. Reprinted in Cantor [1932] 1962, 252–260. [Cited in outline
12 and item Cantor [1932] 1962.]
———. 1887–1888. Mitteilungen zur Lehre vom Transfiniten. Zeitschrift für Philosophie und
philosophische Kritik 91: 81–125, 92: 240–265. LC: B3.Z44. Reprinted in Cantor [1932] 1962,
378–439. [Cited in outline 15 and item Cantor [1932] 1962.]
———. [1891] 1996. On an elementary question in the theory of manifolds. Translated by
William Ewald. In Ewald 1996, volume 2, section 19.D, 920–922. Originally published as
“Über eine elementare Frage der Mannigfaltigkeitslehre,” Jahresbericht der Deutschen
Mathematiker-Vereinigung 1: 75–78, LC: QA1.D4, Internet: Göttingen, and reprinted in
Cantor [1932] 1962, 278–281. [Cited in outline 15 and items Cantor [1932] 1962 and Ewald
1996.]
———. [1895–1897] 1952. Contributions to the Founding of the Theory of Transfinite Numbers.
Translated and with a preface, introduction, and notes by Philip E. B. Jourdain, New York:
Dover Publications. LC: QA248.C2. Originally published as “Beiträge zur Begründung der
transfinite Mengenlehre,” Mathematische Annalen 46: 481–512, 49: 207–246, LC: QA1.M29,
Internet: Göttingen, and reprinted in G. Cantor [1932] 1962, 282–356. The translation was
originally published in 1915 by the Open Court Publishing Company. [Cited in outline 15 and
item Cantor [1932] 1962.]
———. [1932] 1962. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts,
mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor–
Dedekind. Edited by Ernst Zermelo. With a biography of Cantor by Adolf Fraenkel. Hildesheim:
Georg Olms Verlagsbuchhandlung. LC: QA3.C27. [Cited in items Cantor 1878,
1879–1884, 1884, 1887–1888, [1895–1897] 1952.]
Chicago Manual of Style, The. 1993. Fourteenth edition. Chicago: University of Chicago Press.
LC: Z53.U69. ISBN: 0-226-10389-7. [Cited in this bibliography’s introduction.]
Church, Alonzo. 1956. Introduction to Mathematical Logic. Princeton: Princeton University
Press. LC: BC135.C47. MSN: Gál. Although the title page says volume one, there has never
been a volume two. [Cited in outline 33.]
Cohen, Leon W., and Gertrude Ehrlich. 1963. The Structure of the Real Number System.
Princeton: D. Van Nostrand. LC: QA241.C67. JSL 34(1969): K. Segerberg. [Cited in the Basic
Set Theory unit.]
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Page 4 MATH 800 BIBLIOGRAPHY SPRING 2008
Cohen, Paul J. 1963. The independence of the continuum hypothesis. Proceedings of the
National Academy of Sciences of the United States of America 50: 1143–1148, 51: 105–110.
LC: Q11.N26. Internet: JSTOR. MSN: A. Mostowski. [Cited in outline 17.]
Conway, John Horton. 1973. Effective implications between the “finite” choice axioms. In
Mathias and Rogers 1973, 439–458. MSN: R. C. Lyndon. [Cited in outline 17.]
Cooke, W. P. 1969. “Rye whiskey” in contrapositive. American Mathematical Monthly 76: 1051.
LC: QA1.A51. Internet: JSTOR. [Cited in outline 29.]
Daub en, Joseph. 1979. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton:
Princeton University Press. LC: QA248.D27. ISBN: 0-691-08583-8. MSN: H. C. Kennedy.
[Cited in outline 10.]
Davis, Martin. 1958. Computability and Unsolvability. New York: McGraw–Hill Book Company.
LC: QA248.5.D3. MSN: E. Burger. [Cited in outline 12.]
Dedekind, Richard. [1888] 1963. The nature and meaning of numbers. In Dedekind [1901] 1963,
29–115. Reprinted, extensively revised, in Ewald 1996, volume 2, 787–833. Originally
published as Was sind und was sollen die Zahlen, Braunschweig: F. Vieweg, 1888, reprinted
in Dedekind 1930–1932b, volume 3, 335–391. [Cited in the Natural Numbers unit, outlines
9, 17, and items Dedekind [1901] 1963, 1930–1932b, and Ewald 1996.]
———. [1901] 1963. Essays on the Theory of Numbers. Translated by W. W. Beman. New York:
Dover Publications. LC: QA248.D3. Originally published by Open Court (La Salle, Illinois)
in 1901. Reprinted, extensively revised, in Ewald 1996, 765–779,787–833. [Cited in items
Dedekind [1888] 1963 and Ewald 1996.]
———. 1930–1932a. Ähnliche (deutliche) Abbildung und ähnliche Systeme: 1887.7.11. in Dedekind
1930–1932b, volume 3, 447–449. Unpublished manuscript. [Cited in outlines 12, 17.]
———. 1930–1932b. Gesammelte mathematische Werke. Three volumes. Edited by Robert
Fricke, Emmy Noether, and Øystein Ore. Braunschweig: Friedrich Vieweg & Sohn. LC:
QA36.D4. Internet: Göttingen. [Cited in items Dedekind [1888] 1963 and 1930–1932a.]
Enderton, Herbert. 1972. A mathematical introduction to logic. New York: Academic Press.
[Cited in outline ??.]
Enriques, Federigo. 1907. Prinzipien der Geometrie. In Meyer and Mohrmann 1907–1934, part
1, half 1, 1–129. Article III A, B 1. [Cited in outline 12 and item Meyer and Mohrmann
1907–1934.]
Ewald, William B., editor. 1996. From Kant to Hilbert: A Source Book in the Foundations of
Mathematics. Two volumes. Oxford: Clarendon Press. LC: QA8.6.F77. ISBN: 0-198-50537-X.
[Cited in item Cantor [1891] 1996.]
Feferman, Anita B., and Solomon Feferman. 2004. Alfred Tarski: Life and Logic. Cambridge,
England: Cambridge University Press. LC: QA29.T32.F44. ISBN: 0-521-80240-7. MSN: J.
W. Dauben. Reviewed in Sinaceur 2007, Wells 2007. Several other reviews are accessible via
Internet: JSTOR. [Cited in outline 9 and items Sinaceur 2007 and Wells 2007.]
Ferreirós Domínguez, José. 1999. Labyrinth of Thought: A History of Set Theory and Its Role
in Modern Mathematics. Basel: Birkhäuser Verlag. LC: QA248.F467. ISBN: 3-764-35749-5.
MSN: E. Mendelson. [Cited in outline 10.]
Finberg, David, Matteo Mainetti, and Gian-Carlo Rota. 1996. The logic of commuting equivalence
relations. In Ursini and Aglianò 1996, 69–96. MSN: Y. Rav. [Cited in outline 3 and in
item Ursini and Aglianò 1996.]
Flanders, Harley. 1987. Generating posets. College Mathematics Journal 18: 323–327. LC:
QA11.A1.T9. Internet: JSTOR. [Cited in outline 5.]
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MATH 800 BIBLIOGRAPHY SPRING 2008 Page 5
Fraenkel, Abraham A. 1961. Abstract Set Theory. Second, revised edition. Amsterdam: North-
Holland Publishing Company. LC: QA248.F74. MSN: F. Bagemihl. JSL 28(1963): 168–169
A. Church. [Cited in the Cardinals II unit.]
Franzén, Torkel. 2005. Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse. Wellesley,
Massachusetts: A K Peters. LC: QA9.65.F73. ISBN: 1-56881-238-8. MSN: W. Sieg. [Cited
in the Gödel’s and Tarski’s Theorems unit.]
Frege, Gottlob. [1895] 1980. A critical elucidation of some points in E. Schroeder’s Vorlesungen
ueber die Algebra der Logik. In Frege 1980, 86–106. Originally published as “Kritische
Beleuchtung einiger Punkte in E. Schröders Vorlesung über die Algebra der Logik,” Archiv
für systematische Philosophie und Soziologie (new series) 1: 433–456, LC: B3.A7. [Cited in
outline 17 and item Frege 1980.]
———. [1902] 1970. Letter to Russell. Translated by Beverly Woodward. In Heijenoort [1967]
1970, 126–128. Response to Russell [1902] 1970. [Cited in item Russell [1902] 1970.]
———. 1980. Translations from the Philosophical Writings of Gottlog Frege. Third edition.
Edited by Peter Geach and Max Black, with index by E. D. Klemke. Oxford: Basil Blackwell.
LC: QA8.4.F73. ISBN: 0-631-12911-1. JSL 18(1953): 92–93 A. Church; JSL 46(1981): 870
–871 C. Parsons. [Cited in item Frege [1895] 1980.]
Frewer, M. 1981. Felix Bernstein. Jahresbericht der Deutschen Mathematiker-Vereinigung 83:
84–95. LC: QA1.D4. Internet: Bielefeld. [Cited in outline 12.]
Galvin, Fred. 1994. A proof of Dilworth’s chain decomposition theorem. American Mathematical
Monthly 101: 352–353. LC: QA1.A51. Internet: JSTOR. MSN: Anonymous. [Cited in outline
5.]
George, Alexander. 1987. The imprecision of impredicativity. Mind 96: 514–518. LC: B1.M5.
Internet: JSTOR. [Cited in the Natural Numbers unit.]
Gillman, Leonard. 2002–2003. Two classical surprises concerning the axiom of choice and the
continuum hypothesis. American Mathematical Monthly 109: 544–553, 110: 79–80. LC:
QA1.A51. Internet: JSTOR. [Cited in outline 23.]
Gödel, Kurt. [1931] 1967. On formally undecidable propositions of Principia Mathematica and
related systems I. Translated by Jean van Heijenoort. In Heijenoort [1967] 1970, 592 – 617.
Originally published as “Über formal unentscheidbare Sätze der Principia Mathematica und
verwandter Systeme I,” Monatshefte für Mathematik 38: 173–198. There is no part II. [Cited
the Gödel’s and Tarski’s Theorems unit and item Heijenoort [1967] 1970.]
———. 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:
556–557. LC: Q11.N26. Internet: JSTOR. JSL 5(1940): 116–117 P. Bernays. [Cited in outline
17.]
———. 1947. What is Cantor’s continuum problem? American Mathematical Monthly 14:
515–525. LC: QA1.A51. Internet: JSTOR. MSN: B. Jónsson. JSL 13(1948): 116–117 S.
Kleene. [Cited in the Cardinals II unit and outline 23.]
Grattan-Guinness, Ivor. 2000. The Search for Mathematical Roots 1870–1940: Logics, Set
Theories and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton:
Princeton University Press. LC: QA248.G684. ISBN: 0-691-05857-1. MSN: R. Murawski.
[Cited in outline 10, 12.]
Harris, John H. 1970. On a problem of Th. Skolem. Notre Dame Journal of Formal Logic 11:
372–374. LC: BC1.N6. Internet: Euclid. MSN: N. H. Williams. JSL 36(1971): 680 Jean
Rubin. [Cited in outline 1.]
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Page 6 MATH 800 BIBLIOGRAPHY SPRING 2008
Hartogs, Fritz. 1915. Über das Problem der Wohlordnung. Mathematische Annalen 76: 438–
443. LC: QA1.M29. Internet: Göttingen. [Cited in the Cardinals II unit.]
Hausdorff, Felix. 1914. Grundzüge der Mengenlehre. Leipzig: Von Veit. LC: QA248.H4. There
have been several later editions and translations. [Cited in outline 20 and the Maximal
Principles unit.]
Heijenoort, Jean van. [1967] 1970. From Frege to Gödel: A Source Book in Mathematical Logic,
1879–1931. Cambridge, Massachusetts: Harvard University Press. LC: QA9.V3. ISBN: 0-674-
32449-8. MSN: J. W. Dawson. JSL 37(1972): 405, A. Church, 39(1974): 355 A. Church. [Cited
in outline 1 and items Burali-Forti [1897] 1970, Frege [1902] 1970, Gödel [1931] 1967, Russell
[1902] 1970, and Zermelo [1904] 1970, [1908] 1970a, [1908] 1970b.]
Heine, Edouard. 1872. Die Elemente der Functionenlehre. Journal für die reine und angewandte
Mathematik 74: 172–188. LC: QA1.J6. Internet: Göttingen. [Cited in outline 17.]
Heise, Werner. 1971. Das Lemma von Zorn: Eine vergleichende Untersuchung geometrischer,
algebraischer und topologischer Hüllensysteme. Mathematisch-physikalische Semesterberichte
(new series) 19: 73–82. LC: QA1.M288. MSN: A. Appert. [Cited in the Maximal Principles
unit.]
Hessenberg, Gerhard. 1906. Grundbegriffe der Mengenlehre: zweite Bericht über das Unendliche
in der Mathematik. Abhandlungen der Fries’schen Schule (new series) 1 (4): 1–220. LC:
B3.A3. [Cited in the Cardinals II unit and outline 12.]
Hilbert, David. [1900] 2000. Mathematical problems. Translated by Mary Winston Newson.
Bulletin of the American Mathematical Society (new series) 37: 407– 436. LC: QA1.A52.
Internet: AMS. Reprinted from Bulletin of the American Mathematical Society, 8 (1902):
437– 479. Originally published as “Mathematische Probleme,” Nachrichten von der Königlichen
Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse 1900:
253–297, LC: AS182.G348, Internet: Göttingen. A shorter French version is included in
International Congress of Mathematicians [1900] 1902, 58–114. [Cited in outline 17 and items
Hilbert [1932–1935] and International Congress of Mathematicians [1900] 1902.]
Holmes, M. Randall. [1998] 2007. Elementary Set Theory with a Universal Set. Cahiers du
Centre de Logique, 10. Second edition manuscript. Available on the Internet at http://
math.boisestate.edu/~holmes/holmes/nf.html. Originally published by Bruylant–
Academia. Reviewed in Jones 2007. [Cited in outline 2 and item Jones 2007.]
Hönig, Chaim Samuel. 1954. Proof of the Well-ordering of Cardinal Numbers. Proceedings of
the American Mathematical Society 5: 312. LC: QA1.A526. MSN: G. Kurepa. [Cited in the
Cardinals II unit.]
International Congress of Mathematicians. [1900] 1902. Compte rendu du Deuxième Congrès
International des Mathématiciens tenu à Paris du 6 au 12 Aout 1900. Procès-verbaux et communications.
Edited by Ernest Duporcq. Paris: Gauthier–Villars. LC: QA1.I8. Reviewed in
Scott 1900–1901. [Cited in entries Hilbert [1900] 2000, Scott 1900–1901.]
International Congress of Mathematicians. [1928] 1930. Atti del Congresso Internazionale dei
Matematici, Bologna, 3–10 Settembre 1928. Six volumes. Bologna: Nicola Zanichelli Editore,
1930. LC: QA1.I8. [Cited in item Tarski [1928] 1930.]
Iseki, Kiyoshi. 1950. On a proposition which is equivalent to the axiom of choice. Journal of
the Osaka Institute of Science and Technology, Part I 2: 109. LC: QA1.F86. MSN: T. Viola.
[Cited in the Cardinals II unit.]
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MATH 800 BIBLIOGRAPHY SPRING 2008 Page 7
Jech, Thomas. 1994. On Gödel’s second incompleteness theorem. Proceedings of the American
Mathematical Society 121: 311–313. LC: QA1.A526. MSN: Surma. [Cited in the Gödel’s and
Tarski’s Theorems unit.]
Jones, Robert. 2007. Review of Holmes [1998] 2007. Mathematical Intelligencer 29: 71–73. LC:
QA1.M23. [Cited in item Holmes [1998] 2007.]
Jourdain, Philip E. B. 1904a. On the transfinite cardinal numbers of well-ordered aggregates.
London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (sixth series)
7: 61–75. LC: QC1.P3. [Cited in outline 12.]
———. 1904b. On the transfinite cardinal numbers of number-classes in general. London,
Edinburgh, and Dublin Philosophical Magazine and Journal of Science (sixth series) 7:
294–303. LC: QC1.P3. [Cited in outline 12.]
Kanamori, Akihiro. 1997. The mathematical import of Zermelo’s well-ordering theorem.
Bulletin of Symbolic Logic 3: 281–311. LC: QA9.A1.B89. Internet: JSTOR. MSN: Y. Rav.
[Cited in outlines 15 and 21.]
Kennedy, Hubert C. 1973. What Russell learned from Peano. Notre Dame Journal of Formal
Logic 14: 367–372. LC: BC1.N6. Internet: Euclid. MSN: K. Inoue. [Cited in outline 17.]
Knaster, Bronis³aw, and Alfred Tarski. 1927. Un théorème sur les fonctions d’ensembles.
Annales de la Société Polonaise des Mathématiques 6: 133–134. LC: QA1.P59. [Cited in
outline 15.]
Kneser, Hellmuth. 1950. Eine direkte Ableitung des Zornschen Lemmas aus dem Auswahlaxiom.
Mathematische Zeitschrift 53: 110–113. LC: QA1.M3. Internet: Göttingen. MSN: A. D.
Wallace. [Cited in the Maximal Principles unit.]
Kosmák, Ladislav. 1980. On equivalence relations. Acta Mathematica Universitatis Comenianæ
39: 19–23. LC: QA3.B75.A3. Internet: Göttingen. MSN: D. Kurepa. [Cited in outline 3.]
Kraus, G. A. 1968. Motivation for defining the conditional. American Mathematical Monthly
75: 1103–1104. LC: QA1.A51. Internet: JSTOR. [Cited in outline 6.]
Kuratowski, Casimir. 1921. Sur la notion de l’ordre dans la Théorie des Ensembles. Fundamenta
Mathematicæ 2: 161–171. LC: QA1.F8. Internet: Poland. [Cited in outline 1 and the
Virtual Classes unit.]
———. 1922. Une méthode d’élimination des nombres transfinis des raisonnements mathématiques.
Fundamenta Mathematicæ 3: 76–108. LC: QA1.F8. Internet: Poland. [Cited in
outline 21 and the Maximal Principles unit.]
Kurepa, Djuro. 1952. Sur la relation d’inclusion et l’axiome de choix de Zermelo. Bulletin de
la Société Mathématique de France 80: 225–232. LC: QA1.S63. Internet: NUMDAM. MSN:
E. W. Beth. [Cited in the Maximal Principles unit.]
Kurosh, Aleksandr Gennadievich. 1963. Lectures on General Algebra. Translated by Kurt
August Hirsch. New York: Chelsea Publishing Company. LC: QA155.K813. [Cited in the
Equivalences and Partitions, Partially Ordered Sets, and Complete Lattices unit.]
Levi, Beppo. 1902. Intorno alla teoria degli aggregati. Reale Istituto Lombardo di Scienze e
Lettere: Rendiconti (series 2) 35: 863–868. LC: AS222.I42. [Cited in outline 17.]
Lightstone, A. H. 1965. Symbolic Logic and the Real Number System. New York: Harper & Row,
Publishers. LC: QA255.L55. [Cited in the Paper Topics list.]
Lipschutz, Seymour. 1964. Schaum’s Outline of Theory and Problems of Set Theory and Related
Topics. New York: McGraw–Hill. LC: QA248.L57. ISBN: 0-070-38159-3. [Cited in the Basic
Set Theory unit.]
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Page 8 MATH 800 BIBLIOGRAPHY SPRING 2008
Lipton, James. 1991. An Exaltation of Larks: The Ultimate Edition. New York: Viking Penguin.
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Monk, J. Donald. 1969. Introduction to Set Theory. New York: McGraw–Hill. LC: QA248.M53.
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[Cited in the Natural Numbers unit.]
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