%2345678901234567890123456789012345678901234567890123456789012345678901234567890 @book{Albers, editor = "Donald J. Albers and G. L. Alexanderson", title = "Mathematical People", publisher = "Contemporary Books, Inc.", address = "Chicago", note = "[QA28.M37]", year = 1985 } @book{Anderson, author = "Alan Ross Anderson and Nuel D. Belnap", title = "Entailment", publisher = "Princeton University Press", address = "Princeton", volume = 1, note = "[QA9.A634 1975 v.1]", year = 1975} @book{Barrow, author = "John D. Barrow", title = "Theories of Everything: The Quest for Ultimate Explanation", publisher = "Oxford University Press", address = "Oxford", note = "[Q175.B225]", year = 1991 } @book{Behnke, editor = "H. Behnke and F. Backmann and K. Fladt and W. S{\"{u}}ss", title = "Fundamentals of Mathematics", volume = "I", publisher = "The MIT Press", address = "Cambridge, Massachusetts", note = "[QA37.2.B413]", year = 1974 } @book{Bell, author = "J. L. Bell and M. Machover", title = "A Course in Mathematical Logic", publisher = "North-Holland", address = "Amsterdam", note = "[QA9.B3953]", year = 1977 } @inproceedings{Blass, author = "Andrea Blass", title = "The Interaction Between Category Theory and Set Theory", pages = "5--29", booktitle = "Mathematical Applications of Category Theory (Proceedings of the Special Session on Mathematical Applications Category Theory, 89th Annual Meeting of the American Mathematical Society, held in Denver, Colorado January 5--9, 1983)", editor = "John Walter Gray", year = 1983, note = "[QA169.A47 1983]", publisher = "American Mathematical Society", address = "Providence, Rhode Island"} @proceedings{Bledsoe, editor = "W. W. Bledsoe and D. W. Loveland", title = "Automated Theorem Proving: After 25 Years (Proceedings of the Special Session on Automatic Theorem Proving, 89th Annual Meeting of the American Mathematical Society, held in Denver, Colorado January 5--9, 1983)", year = 1983, note = "[QA76.9.A96.S64 1983]", publisher = "American Mathematical Society", address = "Providence, Rhode Island" } @book{Boolos, author = "George S. Boolos and Richard C. Jeffrey", title = "Computability and Log\-ic", publisher = "Cambridge University Press", edition = "third", address = "Cambridge", note = "[QA9.59.B66 1989]", year = 1989 } @book{Campbell, author = "John Campbell", title = "Programmer's Progress", publisher = "White Star Software", address = "Box 51623, Palo Alto, CA 94303", year = 1991 } @inproceedings{Chou, author = "Shang-Ching Chou", title = "Proving Elementary Geometry Theorems Using {W}u's Algorithm", pages = "243--286", booktitle = "Automated Theorem Proving: After 25 Years (Proceedings of the Special Session on Automatic Theorem Proving, 89th Annual Meeting of the American Mathematical Society, held in Denver, Colorado January 5--9, 1983)", editor = "W. W. Bledsoe and D. W. Loveland", year = 1983, note = "[QA76.9.A96.S64 1983]", publisher = "American Mathematical Society", address = "Providence, Rhode Island" } @incollection{Courant, author = "Richard Courant and Herbert Robbins", title = "Topology", pages = "573--590", booktitle = "The World of Mathematics, Volume One", editor = "James R. Newman", publisher = "Simon and Schuster", address = "New York", note = "[QA3.W67 1988]", year = 1956 } @book{Curry, author = "Haskell B. Curry", title = "Foundations of Mathematical Logic", publisher = "Dover Publications, Inc.", address = "New York", note = "[QA9.C976 1977]", year = 1977 } @book{Davis, author = "Philip J. Davis and Reuben Hersh", title = "The Mathematical Experience", publisher = "Birkh{\"{a}}user Boston", address = "Boston", note = "[QA8.4.D37 1982]", year = 1981 } @incollection{deMillo, author = "Richard de Millo and Richard Lipton and Alan Perlis", title = "Social Processes and Proofs of Theorems and Programs", pages = "267--285", booktitle = "New Directions in the Philosophy of Mathematics", editor = "Thomas Tymoczko", publisher = "Birkh{\"{a}}user Boston, Inc.", address = "Boston", note = "[QA8.6.N48 1986]", year = 1986 } @book{Edwards, author = "Robert E. Edwards", title = "A Formal Background to Mathematics", publisher = "Springer-Verlag", address = "New York", note = "[QA37.2.E38 v.1a]", year = 1979 } @book{Enderton, author = "Herbert B. Enderton", title = "Elements of Set Theory", publisher = "Academic Press, Inc.", address = "San Diego", note = "[QA248.E5]", year = 1977 } @book{Goodstein, author = "R. L. Goodstein", title = "Development of Mathematical Logic", publisher = "Springer-Verlag New York Inc.", address = "New York", note = "[QA9.G6554]", year = 1971 } @book{Guillen, author = "Michael Guillen", title = "Bridges to Infinity", publisher = "Jeremy P. Tarcher, Inc.", address = "Los Angeles", note = "[QA93.G8]", year = 1983 } @book{Hamilton, author = "Alan G. Hamilton", title = "Logic for Mathematicians", edition = "revised", publisher = "Cambridge University Press", address = "Cambridge", note = "[QA9.H298]", year = 1988 } @unpublished{Harrison, author = "John Robert Harrison", title = "Metatheory and Reflection in Theorem Proving: A Survey and Critique", note = "Technical Report CRC-053. SRI Cambridge, Millers Yard, Cambridge, UK, 1995. Available on the Web as {\verb+http:+}\-{\verb+//www.cl.cam.ac.uk/users/jrh/papers/reflect.html+}"} @TECHREPORT{Harrison-thesis, author = "John Robert Harrison", title = "Theorem Proving with the Real Numbers", institution = "University of Cambridge Computer Lab\-o\-ra\-to\-ry", address = "New Museums Site, Pembroke Street, Cambridge, CB2 3QG, UK", year = 1996, number = 408, type = "Technical Report", note = "Author's PhD thesis, available on the Web at {\verb+http:+}\-{\verb+//www.cl.cam.ac.uk+}\-{\verb+/users+}\-{\verb+/jrh+}% \-{\verb+/papers+}\-{\verb+/thesis.html+}"} @book{Herrlich, author = "Horst Herrlich and George E. Strecker", title = "Category Theory: An Introduction", publisher = "Allyn and Bacon Inc.", address = "Boston", note = "[QA169.H567]", year = 1973 } @article{Hindley, author = "J. Roger Hindley and David Meredith", title = "Principal Type-Schemes and Condensed Detachment", journal = "The Journal of Symbolic Logic", volume = 55, year = 1990, note = "[QA.J87]", pages = "90--105" } @book{Hofstadter, author = "Douglas R. Hofstadter", title = "G{\"{o}}del, Escher, Bach", publisher = "Basic Books, Inc.", address = "New York", note = "[QA9.H63 1980]", year = 1979 } @article{Kalish, author = "D. Kalish and R. Montague", title = "On {T}arski's Formalization of Predicate Logic with Identity", journal = "Archiv f{\"{u}}r Mathematische Logik und Grundlagenfor\-schung", volume = 7, year = 1965, note = "[QA.A673]", pages = "81--101" } @article{Kalman, author = "J. A. Kalman", title = "Condensed Detachment as a Rule of Inference", journal = "Studia Logica", volume = 42, number = 4, year = 1983, note = "[B18.P6.S933]", pages = "443-451" } @book{Kline, author = "Morris Kline", title = "Mathematical Thought from Ancient to Modern Times", publisher = "Oxford University Press", address = "New York", note = "[QA21.K516 1990 v.3]", year = 1972 } @book{Klinel, author = "Morris Kline", title = "Mathematics, The Loss of Certainty", publisher = "Oxford University Press", address = "New York", note = "[QA21.K525]", year = 1980 } @book{Kramer, author = "Edna E. Kramer", title = "The Nature and Growth of Modern Mathematics", publisher = "Princeton University Press", address = "Princeton, New Jersey", note = "[QA93.K89 1981]", year = 1981 } @book{Landau, author = "Edmund Landau", title = "Foundations of Analysis", publisher = "Chelsea Publishing Company", address = "New York", edition = "second", note = "[QA241.L2541 1960]", year = 1960 } @article{Leblanc, author = "Hugues Leblanc", title = "On {M}eyer and {L}ambert's Quantificational Calculus {FQ}", journal = "The Journal of Symbolic Logic", volume = 33, year = 1968, note = "[QA.J87]", pages = "275--280" } @article{Lejewski, author = "Czeslaw Lejewski", title = "On Implicational Definitions", journal = "Studia Logica", volume = 8, year = 1958, note = "[B18.P6.S933]", pages = "189--208" } @book{Margaris, author = "Angelo Margaris", title = "First Order Mathematical Logic", publisher = "Blaisdell Publishing Company", address = "Waltham, Massachusetts", note = "[QA9.M327]", year = 1967} @book{Manin, author = "Yu I. Manin", title = "A Course in Mathematical Logic", publisher = "Springer-Verlag", address = "New York", note = "[QA9.M29613]", year = "1977" } @article{Mathias, author = "Adrian R. D. Mathias", title = "A Term of Length 4,523,659,424,929", journal = "Synthese", volume = 133, year = 2002, note = "[Q.S993]", pages = "75--86" } @article{Megill, author = "Norman D. Megill", title = "A Finitely Axiomatized Formalization of Predicate Calculus with Equality", journal = "Notre Dame Journal of Formal Logic", volume = 36, year = 1995, note = "[QA.N914]", pages = "435--453" } @unpublished{Megillc, author = "Norman D. Megill", title = "A Shorter Equivalent of the Axiom of Choice", month = "June", note = "Unpublished", year = 1991 } @article{MegillBunder, author = "Norman D. Megill and Martin W. Bunder", title = "Weaker {D}-Complete Logics", journal = "Journal of the IGPL", volume = 4, year = 1996, pages = "215--225", note = "Available on the Web at {\verb+http:+}\-{\verb+//www.mpi-sb.mpg.de+}\-{\verb+/igpl+}% \-{\verb+/Journal+}\-{\verb+/V4-2+}\-{\verb+/#Megill+}"} } @book{Mendelson, author = "Elliott Mendelson", title = "Introduction to Mathematical Logic", edition = "second", publisher = "D. Van Nostrand Company, Inc.", address = "New York", note = "[QA9.M537 1979]", year = 1979 } @article{Meredith, author = "David Meredith", title = "In Memoriam {C}arew {A}rthur {M}eredith (1904-1976)", journal = "Notre Dame Journal of Formal Logic", volume = 18, year = 1977, note = "[QA.N914]", pages = "513--516" } @article{CAMeredith, author = "C. A. Meredith", title = "Single Axioms for the Systems ({C},{N}), ({C},{O}) and ({A},{N}) of the Two-Valued Propositional Calculus", journal = "The Journal of Computing Systems", volume = 3, year = 1953, pages = "155--164" } @article{Monk, author = "J. Donald Monk", title = "Provability With Finitely Many Variables", journal = "The Journal of Symbolic Logic", volume = 27, year = 1971, note = "[QA.J87]", pages = "353--358" } @article{Monks, author = "J. Donald Monk", title = "Substitutionless Predicate Logic With Identity", journal = "Archiv f{\"{u}}r Mathematische Logik und Grundlagenfor\-schung", volume = 7, year = 1965, pages = "103--121" } %% Took out this from above to prevent LaTeX underfull warning: % note = "[QA.A673]", @book{Moore, author = "A. W. Moore", title = "The Infinite", publisher = "Routledge", address = "New York", note = "[BD411.M59]", year = 1989} @book{Munkres, author = "James R. Munkres", title = "Topology: A First Course", publisher = "Prentice-Hall, Inc.", address = "Englewood Cliffs, New Jersey", note = "[QA611.M82]", year = 1975} @article{Nemesszeghy, author = "E. Z. Nemesszeghy and E. A. Nemesszeghy", title = "On Strongly Creative Definitions: A Reply to {V}. {F}. {R}ickey", journal = "Logique et Analyse (N.\ S.)", year = 1977, volume = 20, note = "[BC.L832]", pages = "111--115" } @unpublished{Nemeti, author = "N{\'{e}}meti, I.", title = "Algebraizations of Quantifier Logics, an Overview", note = "Version 11.4, preprint, Mathematical Institute, Budapest, 1994. A shortened version without proofs appeared in ``Algebraizations of quantifier logics, an introductory overview,'' {\em Studia Logica}, 50:485--569, 1991 [B18.P6.S933]"} @article{Pavicic, author = "M. Pavi{\v{c}}i{\'{c}}", title = "A New Axiomatization of Unified Quantum Logic", journal = "International Journal of Theoretical Physics", year = 1992, volume = 31, note = "[QC.I626]", pages = "1753 --1766" } @book{Penrose, author = "Roger Penrose", title = "The Emperor's New Mind", publisher = "Oxford University Press", address = "New York", note = "[Q335.P415]", year = 1989 } @book{PetersonI, author = "Ivars Peterson", title = "The Mathematical Tourist", publisher = "W. H. Freeman and Company", address = "New York", note = "[QA93.P475]", year = 1988 } @article{Peterson, author = "Jeremy George Peterson", title = "An automatic theorem prover for substitution and detachment systems", journal = "Notre Dame Journal of Formal Logic", volume = 19, year = 1978, note = "[QA.N914]", pages = "119--122" } @book{Quine, author = "Willard Van Orman Quine", title = "Set Theory and Its Logic", edition = "revised", publisher = "The Belknap Press of Harvard University Press", address = "Cambridge, Massachusetts", note = "[QA248.Q7 1969]", year = 1969 } @article{Robinson, author = "J. A. Robinson", title = "A Machine-Oriented Logic Based on the Resolution Principle", journal = "Journal of the Association for Computing Machinery", year = 1965, volume = 12, pages = "23--41" } @article{RobinsonT, author = "T. Thacher Robinson", title = "Independence of Two Nice Sets of Axioms for the Propositional Calculus", journal = "The Journal of Symbolic Logic", volume = 33, year = 1968, note = "[QA.J87]", pages = "265--270" } @book{Rucker, author = "Rudy Rucker", title = "Infinity and the Mind: The Science and Philosophy of the Infinite", publisher = "Bantam Books, Inc.", address = "New York", note = "[QA9.R79 1982]", year = 1982 } @book{Russell, author = "Bertrand Russell", title = "Mysticism and Logic, and Other Essays", publisher = "Barnes \& Noble Books", address = "Totowa, New Jersey", note = "[B1649.R963.M9 1981]", year = 1981 } @article{Russell2, author = "Bertrand Russell", title = "Recent Work on the Principles of Mathematics", journal = "International Monthly", volume = 4, year = 1901, pages = "84"} @book{Shoenfield, author = "Joseph R. Shoenfield", title = "Mathematical Logic", publisher = "Addison-Wesley Publishing Company, Inc.", address = "Reading, Massachusetts", year = 1967, note = "[QA9.S52]" } @book{Smullyan, author = "Raymond M. Smullyan", title = "Theory of Formal Systems", publisher = "Princeton University Press", address = "Princeton, New Jersey", year = 1961, note = "[QA248.5.S55]" } @book{Solow, author = "Daniel Solow", title = "How to Read and Do Proofs: An Introduction to Mathematical Thought Process", publisher = "John Wiley \& Sons", address = "New York", year = 1982, note = "[QA9.S577]" } @book{Stark, author = "Harold M. Stark", title = "An Introduction to Number Theory", publisher = "Markham Publishing Company", address = "Chicago", note = "[QA241.S72 1978]", year = 1970 } @article{Swart, author = "E. R. Swart", title = "The Philosophical Implications of the Four-Color Problem", journal = "American Mathematical Monthly", year = 1980, volume = 87, month = "November", note = "[QA.A5125]", pages = "697--707" } @book{Takeuti, author = "Gaisi Takeuti and Wilson M. Zaring", title = "Introduction to Axiomatic Set Theory", edition = "second", publisher = "Springer-Verlag New York Inc.", address = "New York", note = "[QA248.T136 1982]", year = 1982} @inproceedings{Tarski, author = "Alfred Tarski", title = "What is Elementary Geometry", pages = "16--29", booktitle = "The Axiomatic Method, with Special Reference to Geometry and Physics (Proceedings of an International Symposium held at the University of California, Berkeley, December 26, 1957 --- January 4, 1958)", editor = "Leon Henkin and Patrick Suppes and Alfred Tarski", year = 1959, publisher = "North-Holland Publishing Company", address = "Amsterdam"} @article{Tarski1965, author = "Alfred Tarski", title = "A Simplified Formalization of Predicate Logic with Identity", journal = "Archiv f{\"{u}}r Mathematische Logik und Grundlagenforschung", volume = 7, year = 1965, note = "[QA.A673]", pages = "61--79" } @book{Tymoczko, title = "New Directions in the Philosophy of Mathematics", editor = "Thomas Tymoczko", publisher = "Birkh{\"{a}}user Boston, Inc.", address = "Boston", note = "[QA8.6.N48 1986]", year = 1986 } @incollection{Wang, author = "Hao Wang", title = "Theory and Practice in Mathematics", pages = "129--152", booktitle = "New Directions in the Philosophy of Mathematics", editor = "Thomas Tymoczko", publisher = "Birkh{\"{a}}user Boston, Inc.", address = "Boston", note = "[QA8.6.N48 1986]", year = 1986 } @manual{Webster, title = "Webster's New Collegiate Dictionary", organization = "G. \& C. Merriam Co.", address = "Springfield, Massachusetts", note = "[PE1628.W4M4 1977]", year = 1977 } @manual{Whitehead, author = "Alfred North Whitehead", title = "An Introduction to Mathematics", year = 1911 } @book{PM, author = "Alfred North Whitehead and Bertrand Russell", title = "Principia Mathematica", edition = "second", publisher = "Cambridge University Press", address = "Cambridge", year = "1927", note = "(3 vols.) [QA9.W592 1927]" } @book{Wolfram, author = "Stephen Wolfram", title = "Mathematica: A System for Doing Mathematics by Computer", edition = "second", publisher = "Addison-Wesley Publishing Co.", address = "Redwood City, California", note = "[QA76.95.W65 1991]", year = 1991 } @book{Wos, author = "Larry Wos and Ross Overbeek and Ewing Lusk and Jim Boyle", title = "Automated Reasoning: Introduction and Applications", edition = "second", publisher = "McGraw-Hill, Inc.", address = "New York", note = "[QA76.9.A96.A93 1992]", year = 1992 } % % %[1] Church, Alonzo, Introduction to Mathematical Logic, % Volume 1, Princeton University Press, Princeton, N. J., 1956. % %[2] Cohen, Paul J., Set Theory and the Continuum Hypothesis, % W. A. Benjamin, Inc., Reading, Mass., 1966. % %[3] Hamilton, Alan G., Logic for Mathematicians, Cambridge % University Press, % Cambridge, 1988. %[6] Kleene, Stephen Cole, Introduction to Metamathematics, D. Van % Nostrand Company, Inc., Princeton (1952). %[13] Tarski, Alfred, "A simplified formalization of predicate % logic with identity," Archiv fur Mathematische Logik und % Grundlagenforschung, vol. 7 (1965), pp. 61-79. %[14] Tarski, Alfred and Steven Givant, A Formalization of Set % Theory Without Variables, American Mathematical Society Colloquium % Publications, vol. 41, American Mathematical Society, % Providence, R. I., 1987. %[15] Zeman, J. J., Modal Logic, Oxford University Press, Oxford, 1973.