Abstract
The relation between thesis advisor and doctoral student can be used to draw up academic genealogies. This article discusses brief genealogies for many of the participants (mainly set theorists) of the conferences in CuraƧao in 1995 and Barcelona in 1996 and of the contributors to this volume. It includes a partial list of students of A. Mostowski, some stories of mathematical beginnings and references for those interested in further study.
This work was partly supported by grants number DMS-9306286 and INT-9503676 from the National Science Foundation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
E. Adcock, Jr. (managing ed.), American Men and Women of Science, 1989ā90, 17th edition, R.R. Bowker, New York, 1989.
J.W. Addison, Eloge: Alfred Tarski: 1901ā1983, Ann. Hist. Comp. 6 (1984) no. 4, 335ā336.
J.W. Addison, private communication, 1997.
D.J. Albers and G.L. Alexanderson, (eds.) Mathematical people: Profiles and inter-views, (Introduction by P.J. Davis) Published in collaboration with the Mathematical Association of America, Birkhaeuser, Boston-Basel-Stuttgart (1985).
D.J. Albers, G.L. Alexanderson, and C. Reid, (eds.) More mathematical people: Contemporary conversations, Harcourt Brace Jovanovich, Publishers, Boston, MA, (1990) and Academic Press, San Diego, CA (1994).
D.J. Albers and C. Reid, An interview with Mary Ellen Rudin, College Math. J. 19 (2) (1988) 114ā137.
W. Aspray, Oswald Veblen and the origins of mathematical logic at Princeton, in: Perspectives on the history of mathematical logic, (T. Drucker, ed), BirkhƤuser, Boston, MA, 1991, 54ā70.
L. Babai, In and out of Hungary: Paul ErdÅs, his friends, and times, in: Combinatorics: Paul ErdÅs is Eighty, (D. MiklÅs, T. SzÅnyi, V.T. SÅs, eds), Bolyai Society Mathematical Studies 2, J. Bolyai Mathmatical Society, Budapest, (1996) 7ā95.
J. Babini, A. GonzĆ”lez Dommguez, and L.A. SantalĆ³, Julio Ray Pastor, Rev. Un. Mat. Argentina 21 (1962) 3ā22.
R. Baer, Zur Axiomatik der Kardinalzahlarithmetik, Mathematische Zeitschrift 29 (1929) 381ā396.
J. Bagaria, Definable Forcing and Regularity properties of projective sets of reals, Ph.D. thesis, University of California, Berkeley, 1991.
H. Barendregt, The impact of the lambda calculus in logic and computer science, Bull. Symbolic Logic 3 (2) (1997) 181ā215.
Y. Bar-Hillel, E.I.J. Poznanski, M.O. Rabin and A. Robinson (eds.), Essays on the foundations of mathematics: Dedicated to A A Fraenkel on his seventieth anniversary (Jerusalem, 1961), The Magnes Press, Hebrew University, Jerusalem, 1961.
J. Barwise, H.J. Keisler and K. Kunen, (eds.) The Kleene Symposium (Proceedings of the Symposium held June 18ā24, 1978 at Madison, Wisconsin), Studies in Logic and the Foundations of Mathematics 101, North-Holland Publishing Company, Amsterdam, New York, Oxford (1980).
J.E. Baumgartner, In memorium: Paul ErdÅs, 1913ā1996, J. Symbolic Logic 3 no. 1, (1997) 70ā72.
P. Bernays and D. Hilbert, Grundlagen der Mathematik, 1939 (see pp. 252ā3). (see Kleene for more info)
D. Blackwell, Infinite games and analytic sets, Proc. Natl. Acad. Sci. USA 58, (1967) 1836ā1837.
D. Blackwell, Infinite G Ī“ games with imperfect information, Matematwyki applicationes mathematicae 10 (1969) 99ā101.
D. Blackwell, Borel sets via games, Ann. Probab. 9, (1981) 321ā322.
A. Blass, private communication, 1997.
The Brits Index, Author Index, British Theses Service, Surrey England, 1989.
M.L. Cartwright, Jacques Hadamard, Biographical Memoirs of Fellows of the Royal Society of London, 11 (1965) 75ā99.
G. Choquet, (ed.), Arnaud Denjoy, Ć©vocation de lāhomme et de lāoeuvre, Asterisque 28ā29, (1975).
Rolando Chuaqui Kettlun, Proyecciones 13 (1994) no. 1, iii-iv. (Revista de MatemƔticas, Universidad Catlica del Norte).
R. Chuaqui, Alfred Tarski, mathematician of truth, Bol. Soc. Paran. Mat. (2) 6 (1985) no. 1, 1ā10.
In memorial of Professor Rolando Chuaqui, Notas de la Sociedad de MatemĆ¢tica de Chile 15 (1996) no. 1, vāviii.
K. Ciesielski and Z. Pogoda, Conversation with Andrzej Turowicz, The Mathematical Inteli, 10 (4) (1988) 13ā20.
P.J. Cohen, Set theory and the continuum hypothesis, W.A. Benjamin, New York, 1966.
P. Colling, Dissertation Abstracts International, series B, University Microfilms International, 1980.
R.G. Cooke, Paul Dienes, J. London math. Soc. 35 (1960) 251ā255.
W.W. Comfort, A survey of cardinal invariants, General Topol. Appl. 1 (1971) 163ā199.
E. Corominas, Contribution Ć la thĆ©orie de la dĆ©rivation dāordre supĆ©rieure, Bull. Soc. Math. France 81, (1953) 177ā222.
J.N. Crossley, Reminiscences of logicians, in: Algebra Logic (Papers Summer Res. Inst, Clayton 1974), J.N. Crossley (ed.), Lect. Notes Math. 450 (1975) 1ā62.
J. Dauben, Abraham Robinson: the creation of nonstandard analysis, a personal and mathematical Odyssey, (foreword by B. Mandelbrot), Princeton University Press, Princeton, 1995.
J. Dawson, Logical dilemmas: the life and work of Kurt GÅdel, A. K. Peters, Welles-ley, MA, 1997.
A.G. Debus, World Whoās Who of Science, 1st edition, Marquis-Whoās Who, Chicago, Charles Scribner & Sons, NY, 1981.
M. DeGroot, A conversation with David Blackwell, Statist. Sci. 1 no. 1 (1986) 40ā53.
A. Denjoy, Notice nĆ©crologuique sur M. Hermann Weyl, CR. Acad. Sci. Paris 241 (1955) 1665ā1667.
C. Di Prisco, private communication, 1997.
J.I. Diaz, The work of Alberto Dou in applied mathematics, Proc. Math. Meet, in Honor of A. Dou, Madrid/Spain 1988, (1989) 15ā24.
H.B. Enderton, In memoriam: Alonzo Church (1903ā1995), Bulletin of Symbolic Logic 1 (1995) 486ā488.
P. ErdÅs and A. Hajnal, Unsolved Problems in set theory, in: Axiomatic Set Theory, Proc. Sympos. Pure Math., Univ. of Calif., Los Angeles, Ca., 1967 (D.S. Scott, ed.), Amer. Math. Soc, Providence, RI, 13 (1971) no. I, 17ā48.
P. ErdÅs and A. Hajnal, Solved and Unsolved Problems in Set Theory, in: Proceed- ings of the Tar ski Symposium, Proc. Sympos. Pure Math., Univ. of Calif., Berkeley, Ca., 1971, Amer. Math. Soc, Providence, RI, 25 (1974) no. I, 261ā265.
P. ErdÅs, A. Hajnal, A. MĆ”tĆ© and R. Rado, Combinatorial Set Theory: Partition Re- lations for Cardinals, AkadĆ©miai KiadÅ, Budapest and North-Holland, Amsterdam, New York and Oxford, 1984.
M. FrĆ©chet, Notice nĆ©crologique sur Hadamard, Comptes Rendues Acad. Sci. Paris Ser. A-B 257 (1963), 4081ā4086.
M. FrƩchet, Les Espaces Abstraits, Borel monograph, Paris, 1928.
A.A. Praenkel, Natural numbers as cardinals, Scripta Mathematica, 6 (1939) 69ā79;
A.A. Praenkel, Natural numbers as ordinals, Scripta Mathematica, 7 (1940) 9ā20;
A.A. Praenkel, The recent controversies about the foundations of mathematics, Scripta Mathematica 13 (1947) 17ā36;
A.A. Praenkel, Problems and methods in modern mathematics, Scripta Mathematica. 9 (1943) 5ā18, 81ā84, 162ā168, 245ā255
A.A. Praenkel, Problems and methods in modern mathematics, Scripta Mathematica., 15 (1949) 169ā182.
A.A. Praenkel, Lebenkreise: aus den Erinnerungen eines Jiidischn mathematikers, Deutsche Verlag-Anstalt, Stuttgart, 1967.
G. Gamov, One Two Three ā¦ Infinity: Facts and speculations of science, Dover, 1988.
C.C. Gillispie (ed.), Dictionary of Scientific Biography, Charles Scribnerās Sons, New York, 1975.
S. Givant, A portrait of Alfred Tarski, The Mathematical Intell. 13 (3) (1991), 16ā32.
K.W. Gruenberg, Reinhold Baer, Bull. Lond. Math. Soc. 13, (1981) 339ā361.
M. de Guzman, Humanistic aspects of the work of Alberto Dou, in: Proc. Math. Meet, in Honor of A. Dou, Madrid/Spain 1988, (1989) 25ā31 .
J. Hadamard, LeƧons sur le Calcul des variations, Hermann, Paris, 1910.
J. Hadamard, Les surfaces Ć courbes opposĆ©es et leurs lignes geodĆ©siques, J. Math, pures et appl. (5) 4 (1898) 27ā73.
A. Hajnal, Paul ErdÅsā Set Theory, in: The Mathematics of Paul ErdÅs II, (R.L. Graham and J. Nesetfil, eds.), Algorithms and Combinatorics 14, Springer-Verlag, Berlin, (1997) 352ā393.
G. HasenjƤger, Eine Bemerkung zu Henkinās Beweis fĆ¼r die VollstƤndigkeit des PrƤdikatenkalkĆ¼ls, J. Symbolic Logic 18 (1953) 42ā48.
L. Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949) 159ā166.
J. Henle, An outline of set theory, Springer-Verlag, 1986.
W. Hodges, Step by recursive step: Churchās analysis of effective calculability, Bull. Symbolic Logic 3 (2) (1997) 181ā215.
F. Hodgson, Whoās Who in Science in Europe, third edition, F.H. Books, Limited, Guernsey, Great Britian, 1978.
P. Hilton, Working with Alan Turing, The Mathematical Meli. 13 (4) (1991) 22ā23.
R. Hirsch and V. John-Steiner, A visit to Hungarian mathematics, The Mathematical Intell., 15 (2) (1993) 13ā26.
W. Hodges, Alfred Tarski, J. Symbolic Logic 51 (1986), 866ā868.
A. IviÄ, Z. Mamuzic, Z. Mijajilovic, S. Todorcevic, Selected Papers of Duro Kurepa, Serbian Academy of Sciences and the Arts, Belgrade, 1996.
R. Jensen, private communication, 1997.
J.P. Kahane, Jacques Hadamard, The Mathematical Intell. 13 (1) (1991), 23ā29.
A. Kanamori, The mathematical development of set theory from Cantor to Cohen, Bulletin of Symbolic Logic 2 (1) (1996) 1ā71.
A. Kanamori, The mathematical import of Zermeloās Well-Ordering Theorem, Bulletin of Symbolic Logic, to appear.
D. Kendall, Obituary: Maurice FrĆ©chet, 1978ā1973, J. Roy. Statist. Soc. Ser. A 140 (1977) no. 4, 566.
S. Kleene, Introduction to Metamathematics, North-Holland, Amsterdam, 1952 (see p. 398).
S. Kleene, Gƶdelās impresson on students of logic in the 1930ās, in: Gƶdel Remembered, (P. Weingartner and L. Schmetterer, eds) Bibliopolis, Naples, 1987, 49ā64.
P. Koszmider, private communication, 1997.
H. Kneser, Eine direkte Ableitung des Zornschen Lemmas aus dem Auwahlaxiom, Mathematische Zeitschrift, 53 (1950) 110ā113.
K. Kuratowski, A half century of Polish mathematics, (translated by Andrzej Kirkor from PĆ³lwieku matematyki polskiej 1920ā1970, PWN-Polish Scientific Publishers, Warsawa, 1973), Pergamon Press, Oxford, New York, Toronto, Sydney, Paris, Frankfurt and PWN-Polish Scientific Publishers, Warszawa, 1980.
W. Ledermann, Issai Schur and his school in Berlin, Bull. London Math. Soc. 15 (1983), 97ā106.
A.J. Macintyre, Abraham Robinson 1918ā1974, Bull. Amer. Math. Soc. 83 (1977), 646ā666.
S. Mac Lane, Mathematics at GÅttingen under the Nazis, Notices of the AMS, 42 (10), (1995) 1134ā1138.
S. Mac Lane, Stephen Cole Kleene ā a reminiscence, Annals of Pure Appl. Logic 81 No.1ā3, (1996) 3ā7.
M. Magidor, private communication, 1997.
W. Marek, Bibliography of Andrzej Mostowskiās works, Studia Logica 36 (1977), 3ā8.
W. Marek, private communication, 1997.
D.A. Martin and J.R. Steel, A proof of projective determinacy, J. Amer. Math. Soc. 2 (1989) 71ā125.
J.F. Mauer (managing ed.), Concise Dictionary of Scientific Biography, Charles Scribnerās Sons, New York, 1981.
R.D. Mauldin, ed., The Scottish Book: Mathematics from the Scottish Cafe, BirkhƤuser, Boston, 1981.
W. Mitchell, private communication, 1997.
R. Montague and R. Vaught, Natural models of set theory, Fundamenta Math. 47 (1959) 219ā242.
D. Montgomery, Oswald Veblen, Bull. Amer. Math. Soc. 69 (1963) 26ā36.
G.D. Mostow, Abraham Robinson 1918ā1974, Israel J. of Math. 25 (1976) 4ā14.
Curriculum vitae of A. Mostowski, Set theory and hierarchy theory, Lecture Notes in Math. 537 (Berlin, 1976), 1ā11.
G. MĆ¼ller, Obituary: Paul J. Bernays (1888ā1977), The Mathematical Intell. 1 (1) (1978) 27ā28.
J. Mycielski and H. Steinhaus, A mathematical axiom contradicting the axiom of choice, Bulletin de lāAcadĆ©mie Polonaise des Sciences, SĆ©rie des Sciences MathĆ©matiques, Astronomiques et Physiques, 10 (1962) 1ā3.
J. Mycielski, On the axiom of determinateness I, II, Fund. Math. 53, (1964) 205ā224;
J. Mycielski, On the axiom of determinateness I, II, Fund. Math., 59, (1966) 203ā212.
J. Mycielski, Games with perfect information, in: Handbook of game theory with economic applications, 1, Horth-Holland, Amsterdam, 1992, 41ā70.
M.H.A. Neumann, Obituary: Hermann Weyl, J. London Math. Soc. 33 (1958) 500 ā 511.
K.H. Parshall, Eliakim Hastings Moore and the Founding of an American Mathe- matical Community, 1892ā1902, Annals of Science, 41 (1984) 313ā333.
A. Phillips, Hubert Anson Newton, Bull. Amer. Math. Soc. 3 (1897) 169ā173.
M. Pouzet, Obituary: Ernest Corominas, Order 9 (1992), no. 1, 1ā3.
M. Pouzet, private communication, 1997.
T. Rado, On a simple source for non-computable functions, in: Proc. Symp. Math. Theor. Automata, New York 1962, (1963) 75ā81.
H. Rasiowa, A tribute to A. Mostowski, Logic Colloquium 76, Studies in Logic and Found. Math. 87 (Amsterdam, 1977), 139ā144.
H. Rasiowa, In memory of Andrzej Mostowski, Studia Logica 36 (1977), 1ā3.
C. Reid, Hilbert, Springer-Verlag, New York, Heidelberg, Berlin, second printing, 1972.
C. Richards (ed.), Presentation Ceremony to Professor Richard Rado at the Uni- versity of Reading, May 7, 1971, Bull. Inst. Math. Appl. 7 (1971) 237ā240.
V.F. Rickey, A Survey of LeĆ©niewskiās Logic, Studia Logica 36 (1977) no. 4, 407ā426.
A. Robinson, On the independence of the axiom of definiteness, J. Symbolic Logic 4 (1939), 69ā72.
W.W. Rogosinski, Frederic Riesz, J. London Math. Soc. 31 (4) (1956), 508ā512.
C.A. Rogers, Richard Rado, Biographical Memoirs of Fellows of the Royal Society of London 37 (1991), 413ā426.
J. Roitman, private communication, 1997.
L.A. Santalo, Ernest Corominas (1913ā1992), Rev. Un. Mat. Argentina 38 (1992), no. 1ā2, 157ā158.
J. Schoenfeld, The mathematical work of S. C. Kleene, Bull. Symb. Logic 1, No.l, (1995) 9ā43.
D. Scott, private communication, 1997.
J. Steel, private communication, 1997.
H. Steinhaus, Stefan Banach 1892ā1945, Scripta Math. 26 (1963) 93ā100 (reprinted from Rev. Polish Acad. Sci. vol. V, 1960).
B. SzÅkefalvi-Nagy, F. Riesz: His Life and Style, in: Functions, series, operators, Colloq. Math. Soc. Janos Bolyai 35 (Amsterdam-New York, 1983), 77ā85.
K. Tandori, The Life and Works of Lipot Fejer, in: Functions, series, operators, Colloq. Math. Soc. Janos Bolyai 35 (Amsterdam-New York, 1983), 77ā85.
A. Tarski, Introduction to logic and to the methodology of deductive sciences, Oxford University Press, Oxford and New York, 1941, (enlarged and revised version of a book written in Polish; second, revised edition in 1946).
Proceedings of the Tarski Symposium, (Proc. Sympos. Pure Math., Univ. of Calif., Berkeley, Ca., 1971) Amer. Math. Soc, Providence, RI, 25 (1974) no. I.
F. Tall, The work of Mary Ellen Rudin (Madison, WI, 1991), Ann. New York Acad. Sci. 705, (1993) 1ā16.
S. Todorcevic, private communication, 1997.
D. Reginald Traylor, Creative Teaching: Heritage of R. L. Moore, University of Houston, 1972.
M. Starbird, Mary Ellen Rudin as advisor and geometer, in: The work of Mary Ellen Rudin (Madison, WI, 1991), (F. Tall, ed.), Ann. New York Acad. Sci. 705, (1993) 114ā118.
S. Surma, On the work and influence of Stanislaw Lesniewski, Logic colloquium 76 (Proc. Conf., Oxford 1976), Stud. Logic Found. Math. 87 (1977) 191ā220.
S. Ulam, Adventures of a mathematician, Charles Scribnerās Sons, New York, 1976.
R.L. Vaught, Tarskiās work in model theory, J. Symbolic Logic 51 (1986), 869ā882.
B.L. van der Waerden, The school of Hilbert and Emmy Noether, Bull. London Math. Soc. 15 (1983) 1ā7.
H. Weyl, David Hilbert and his mathematical work, Bull. Amer. Math. Soc. 50, (1944) 612ā654.
D.V. Widder, Joseph Leonard Walsh, SIAM J. Numer. Anal. 3, (1966) 171ā172.
R.L. Wilder, Robert Lee Moore, 1882ā1974, Bull. Amer. Math. Soc. 82, (1976) 417ā427.
R.L. Wilder, The mathematical work of R. L. Moore: its background, nature and influence. Arch. Hist. Exact Sci. 26 (1982) 73ā97.
J. Wolenski, Logic and philosophy in the Lvov-Warsaw school, Kluwer Academic Publishers, Dordrecht and Boston, 1989.
W.H. Woodin, private communication, 1997.
A.D. Young, S. Kochen, S. KÅrner and P. Roquette, Abraham Robinson, Bull. London Math. Soc. 8 (1976) 307ā323.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 1998 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Larson, J.A. (1998). A Picaresque Approach to Set Theory Genealogy. In: Di Prisco, C.A., Larson, J.A., Bagaria, J., Mathias, A.R.D. (eds) Set Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8988-8_9
Download citation
DOI: https://doi.org/10.1007/978-94-015-8988-8_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4978-0
Online ISBN: 978-94-015-8988-8
eBook Packages: Springer Book Archive