@STRING{ zmatl2 = "Zeitschrift f{\"u}r Mathematische Logik und Grundlagen der Mathematik" } @STRING{ traam = "Transactions of the American Mathematical Society" } @STRING{ thec5 = "Theoret. Comput. Sci." } @STRING{ rip = "Revue internationale de philosophie" } @STRING{ repml = "Rep. Math. Logic" } @STRING{ nat = "Die Naturwissenschaften" } @STRING{ mitmg1 = "Mitt. Math. Ges. Hamburg" } @STRING{ mathz = "Mathe\-mati\-sche Zeit\-schrift" } @STRING{ mathj = "Math. Japon." } @STRING{ ma = "Mathe\-ma\-tische An\-nalen" } @STRING{ jsyml = "Journal of Symbolic Logic" } @STRING{ jphil = "Journal of Philosophical Logic" } @STRING{ jp = "Journal of Philosophy" } @STRING{ jdmv = "Jahres\-bericht der Deut\-schen Mathe\-matiker-Ver\-eini\-gung" } @STRING{ jassc = "J.~Assoc. Comput. Mach." } @STRING{ fundm = "Fundamenta Mathematicae" } @STRING{ fundi3 = "Fund. Inform." } @STRING{ bullams = "Bulletin of the American Mathematical Society" } @STRING{ bulapm = "Bull. Acad. Polon. Sci. S{\'e}r. Sci. Math. Astronom. Phys." } @STRING{ bsl = "Bulletin of Symbolic Logic" } @STRING{ aspm = "Annales de la Soci\'et\'e Polonaise de Math\'ematique" } @STRING{ artii = "Artificial Intelligence" } @STRING{ arcml2 = "Archiv f{\"u}r Mathematische Logik und Grundlagenforschung" } @STRING{ annpa = "Annals of Pure and Applied Logic" } @STRING{ amejm = "American Journal of Mathematics" } @STRING{ acarb = "Acad. Roy. Belg." } @STRING{ abhms = "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg" } @ARTICLE{ar:Ackermann24, author = {Wilhelm Ackermann}, year = 1924, title = {Begr\"undung des ``tertium non datur'' mittels der {H}ilbertschen {T}heorie der {W}iderspruchsfreiheit}, journal = ma, volume = 93, pages = {1--36} } @Article{ar:Ackermann40, author = {Wilhelm Ackermann}, title = {Zur {W}iderspruchsfreiheit der {Z}ahlentheorie}, journal = ma, year = 1940, volume = 117, pages = {162--194} } @BOOK{bo:HilbertAckermann28, author = {David Hilbert and Wilhelm Ackermann}, year = 1928, title = {Grundz{\"uge} der theoretischen {L}ogik}, publisher = {Springer}, address = {Berlin} } @PHDTHESIS{th:Behmann18, author = {Heinrich Behmann}, year = 1918, title = {Die {A}ntinomie der transfiniten {Z}ahl und ihre {A}ufl\"osung durch die {T}heorie von {R}ussell und {W}hitehead}, school = {Universit\"at G\"ottingen}, type = {Dissertation}, note = {352 pp.} } @article{ar:Behmann22, author = {Heinrich Behmann}, year = 1922, title = {Beitr\"{a}ge zur {A}lgebra der {L}ogik, insbesondere zum {E}ntscheidungsproblem}, journal = {Mathematische Annalen}, volume = 86, pages = {163--229} } @ARTICLE{ar:Mancosu99, author = {Paolo Mancosu}, year = {1999}, title = {Between {R}ussell and {H}ilbert: {B}ehmann on the foundations of mathematics}, journal = bsl, volume = 5, number = 3, pages = {303--330} } @ARTICLE{ar:vonNeumann27, author = {Johann von Neumann}, year = 1927, title = {Zur {H}ilbertschen {B}eweistheorie}, journal = mathz, volume = 26, pages = {1--46} } @Article{ar:Schroeder-Heister02, author = {Peter Schr{\"o}der-Heister}, title = {Resolution and the origins of structural reasoning: early proof-theoretic ideas of {H}ertz and {G}entzen}, journal = {Bulletin of Symbolic Logic}, year = 2002, volume = 8, pages = {246--265} } @ARTICLE{ar:Sheffer13, author = {Henry Maurice Sheffer}, year = 1913, title = {A set of five independent postulates for boolean algebras, with application to logical constants}, journal = {Transactions of the American Mathematical Society}, volume = 14, pages = {481--488} } @ARTICLE{ar:Sieg99, author = {Wilfried Sieg}, title = {Hilbert's Programs: 1917--1922}, year = {1999}, volume = {5}, number = {1}, pages = {1--44}, journal = bsl } @Article{ar:Zach99, author = {Richard Zach}, title = {Completeness before {P}ost: {B}ernays, {H}ilbert, and the development of propositional logic}, journal = bsl, year = 1999, volume = 5, number = 3, pages = {331--366} } @article{ar:Zach03, author = {Richard Zach}, title = {The practice of finitism. {E}psilon calculus and consistency proofs in {H}ilbert's {P}rogram}, journal = {Synthese}, year = {2003}, volume = {137}, pages = {211-259} } @article{ar:Zach04, author = {Richard Zach}, title = {Hilbert's ``{V}erungl\"uckter {B}eweis,'' the first epsilon-theorem, and consistency proofs}, journal = {History and Philosophy of Logic}, year = 2004, volume = 25, pages = {79--94} } @BOOK{bo:vanHeijenoort67, editor = {Jean van Heijenoort}, year = 1967, title = {From {F}rege to {G}{\"o}del. {A} Source Book in Mathematical Logic, 1897--1931}, publisher = {Harvard University Press}, address = {Cambridge, Mass.} } @BOOK{bo:Mancosu98, editor = {Paolo Mancosu}, year = 1998, title = {From {B}rouwer to {H}ilbert. {T}he Debate on the Foundations of Mathematics in the 1920s}, booktitle = {From Brouwer to Hilbert}, publisher = {Oxford University Press}, address = {Oxford and New York} } @ARTICLE{ar:Hilbert28, author = {David Hilbert}, year = 1928, title = {Die {G}rundlagen der {M}athematik}, journal = {Abhandlungen aus dem Seminar der Hamburgischen Universit{\"a}t}, volume = 6, pages = {65-85}, note = {{E}nglish translation in \cite[464--479]{bo:vanHeijenoort67}}, englishtitle = {The foundations of mathematics} } @BOOK{bo:Ewald96, editor = {William Bragg Ewald}, year = 1996, title = {From {K}ant to {H}ilbert. {A} Source Book in the Foundations of Mathematics}, volume = 2, publisher = {Oxford University Press}, address = {Oxford and New York} } @ARTICLE{ar:Hilbert22, author = {David Hilbert}, year = 1922, title = {Neubegr{\"u}ndung der {M}athematik: {E}rste {M}itteilung}, journal = {Abhandlungen aus dem Seminar der Hamburgischen Universit{\"a}t}, volume = 1, pages = {157--77}, note = {{E}nglish translation in \cite[198--214]{bo:Mancosu98} and \cite[1115--1134]{bo:Ewald96}}, englishtitle = {The new grounding of mathematics. {F}irst report} } @ARTICLE{ar:Hilbert23, author = {David Hilbert}, year = 1923, title = {Die logischen {G}rundlagen der {M}athematik}, journal = ma, volume = 88, pages = {151-165}, note = {{E}nglish translation in \cite[1134--1148]{bo:Ewald96}}, englishtitle = {The logical foundations of mathematics} } @BOOK{bo:HilbertBernays39, author = {David Hilbert and Paul Bernays}, year = 1939, title = {Grundlagen der {M}athematik}, volume = 2, publisher = {Springer}, address = {Berlin} } @Article{ar:Gentzen36, author = {Gerhard Gentzen}, title = {Die {W}iderspruchsfreiheit der reinen {Z}ahlentheorie}, journal = ma, year = 1936, volume = 112, pages = {493--565}, note = {{E}nglish translation in \cite[132--213]{bo:Gentzen69}} } @BOOK{bo:Gentzen69, author = {Gerhard Gentzen}, editor = {M. E. Szabo}, year = 1969, title = {The Collected Papers of {G}erhard {G}entzen}, booktitle = {The Collected Papers of {G}erhard {G}entzen}, publisher = {North-Holland}, address = {Amsterdam} } @Article{ar:Lowenheim15, author = {Leopold L\"{o}wenheim}, title = {\"{U}ber {M}\"oglichkeiten im {R}elativkalk\"{u}l}, journal = ma, year = 1915, pages = {447--470}, note = {English translation in \cite[228--251]{bo:vanHeijenoort67}} }