オンラインで入手できる数理論理学・数学基礎論のテキスト
数理論理学、数学基礎論の教科書的に使えるテキスト（講義ノート、サーヴェイ、モノグラフ等）のうち、オンラインで入手できるものを集めました。
入門的概説 [▲]
- 加茂静夫，「数理論理学（命題論理と述語論理）」．[PDF]
- 嘉田勝，「数理論理学 講義ノート（2013年度版）」．
- Stephen G. Simpson, “Lecture notes: Mathematical Logic.” [PDF]
- Stephen G. Simpson, “Lecture notes: Foundations of Mathematics.” [PDF]
- Yiannis Moschovakis, “Informal notes: Mathematics 220AB.”
- Kenneth Kunen, The Foundations of Mathematics. [PS]
- Itaï Ben Yaacov, “Lecture notes for MATH 770: Foundations of Mathematics.” [PDF]
- Ieke Moerdijk and Jaap van Oosten, “Lecture notes: Sets, Models and Proofs.” [PDF]
- Wolfram Pohlers and Thomas Glaß, An Introduction to Mathematical Logic.
- Wilfried Buchholz, “Lecture notes: Logic I.” [PS]
- Wilfried Buchholz, “Lecture notes: Logic II.” [PDF]
- M. Randall Holmes, “Lecture notes: Proof, Sets and Logic.” [PDF]
- Justus Diller, Einführung in die klassische Prädikatenlogik.
- Martin Ziegler, „Vorlesung über Mathematische Logik.“ [PDF]
論理一般 [▲]
高階論理と型理論 [▲]
- Johan van Benthem and Kees Doets, “Higher-order logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 1, Kluwer, 2001. [PDF]
- 龍田真，「型理論 I」．
- 龍田真，「型理論 II」．
- 龍田真，「型理論 III」．
- 龍田真，「型理論 IV」．
- Per Martin-Löf, Intuitionistic Type Theory, Bibliopolis, 1984. [PDF]
- Bengt Nordström, Kent Petersson and Jan M. Smith,
“Martin-Löf’s type theory” in S. Abramsky, D. Gabbay and T. S. E. Maibaum (eds.), Handbook of Logic in Computer Science, vol. 5, Oxford University Press, 2001. [PDF]
- Bengt Nordström, Kent Petersson and Jan M. Smith, Programming in Martin-Löf’s Type Theory, Oxford University Press, 1990.
直観主義論理 [▲]
- 照井一成，「直観主義論理への招待」．[PDF]
- 鹿島亮，「直観主義論理入門」．[PDF]
- Dirk van Dalen, “Intuitionistic logic” in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell, 2001. [PDF]
- Mark van Atten and Dirk van Dalen, “Intuitionism” in Dale Jaquette (ed.), A Companion to Philosophical Logic, Blackwell, 2002. [PDF]
- Dirk van Dalen, “Intuitionistic logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 5, Kluwer, 2002. [PDF]
コンビネータとラムダ計算 [▲]
- Jean-Louis Krivine, Lambda-Calculus, Types and Models, Ellis Horwood, 1993. [PDF]
- Henk Barendregt, “Lambda calculi with types” in S. Abramsky, D. M. Gabbay and T. S. E. Maibaum (eds.), Handbook of Logic in Compute Science, vol. 2, Oxford University Press, 1993. [PS]
- Harold Simmons and Andrea Schalk, An Introduction to Lambda Calculi and Arithmetic. [PDF]
時相論理および時制論理 [▲]
- Yde Venema, “Temporal logic” in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell, 2001. [PDF]
- Robert Goldblatt, Logics of Time and Computation, 2nd ed., CSLI, 1992.
- Dov Gabbay, Mark Reynolds and Marcelo Finger, “Advanced tense logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 7, Kluwer, 2002. [PDF]
様相論理 [▲]
- 鹿島亮，「チュートリアル：様相論理入門」．[PDF]
- Edward N. Zalta, “Basic concepts in modal logic.” [PDF]
- M. Zakharyaschev, F. Wolter and A. Chagrov, “Advanced modal logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 3, Kluwer, 2001. [PS]
- Patrick. Blackburn, Johan van Benthem and Frank Wolter (eds.), Handbook of Modal Logic, Elsevier, 2007.
- Modal logic: a semantic perspective (by Patrick Blackburn and Johan van Benthem) [PDF]
- Computational modal logic (by Ian Horrocks, Ullrich Hustadt, Ulrike Sattler and Renate Schmidt) [PDF]
- Model theory of modal logic (by Valentin Goranko and Martin Otto) [PDF]
- Algebras and coalgebras (by Yde Venema) [PDF]
- Modal decision problems (by Frank Wolter and Michael Zakharyaschev) [PS]
- Modal consequence relations (by Marcus Kracht) [PDF]
- Higher order modal logic (by Reinhard Muskens) [PDF]
- Modal μ-calculi (by Julien Bradfield and Colin Stirling) [PDF]
- Description logic (by Franz Baader and Carsten Lutz) [PS]
- Hybrid logics (by Carlos Areces and Balder ten Cate) [PDF]
- Combining modal logics (by Agi Kurucz) [PS]
- Automata-theoretic techniques for temporal reasoning (by Moshe Valdi) [PS]
- Applications of modal logic in linguistics (by Lawrence S. Moss and Hans-Joerg Tiede) [PDF]
- Marcus Kracht, Tools and Techniques in Modal Logic, Elsevier, 1999. [PS] ※拡張子がpdfになっていますが、実際にはpsです。
- Robert Goldblatt, Mathematics of Modality, CSLI Publications, 1993.
適切さの論理 [▲]
- Stephen Read, Relevant Logic: A Philosophical Examination of Inference, Basil Blackwell, 1988. [PDF]
- J. Michael Dunn and Greg Restall, “Relevance logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 6, Kluwer, 2002.
自然言語の論理 [▲]
- 緒方典裕，「フォーマルセマンティクス入門」．[PDF]
- Johan van Benthem and G. B. Alice ter Meulen (eds.), Handbook of Logic and Language, MIT Press, 1997.
- Presupposition (by David Beaver) [PS]
- Categorial type logics (by Michael Moortgat) [PDF]
- Representing discourse in context (by Jan van Eijck and Hans Kamp) [PS]
- Temporality (by Mark Steedman) [PS]
- Questions (by Jeroen Groenendijk and Martin Stokhof) [PDF]
- Generics and defaults (by Francis Jeffry Pelletier and Nicholas Asher) [PDF]
- Kai von Fintel and Irene Heim, Intensional Semantics, MIT spring 2011 edition. [PDF]
- Godehard Link, Algebraic Semantics in Language and Philosophy, CSLI Publications, 1998.
- David Beaver, Presupposition and Assertion in Dynamic Semantics, CSLI Publications, 2001. [PDF]
- Francis Jeffry Pelletier and Lenhart K. Schubert, “Mass expressions” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 10, Kluwer, 2003. [PDF]
- Mark Steedman and Jason Baldridge, “Combinatory categorial grammar.” [PDF]
空間論理 [▲]
- Marco Aiello, Ian Pratt-Hartmann and Johan van Benthem (eds.), Handbook of Spatial Logics, Springer, 2007.
- First-order mereotopology (by Ian Pratt-Hartmann) [PDF]
- Algebras, axioms, and topology (by Brandon Bennett and Ivo Düntsch) [PDF]
- Qualitative spatial reasoning using constraint calculi (by Jochen Renz and Bernhard Nebel) [PDF]
- Topology and epistemic logic (by Rohit Parikh, Lawrence S. Moss and Chris Steinsvold) [PDF]
- Logical theories of fragments of elementary geometry (by P. Balbiani, V. Goranko, R. Kellerman and D. Vakarelov) [PDF]
- Locales and toposes as spaces (by Steve Vickers) [PDF]
- Spatial logic + temporal logic = ? (by R. Kontchakov, A. Kurucz, F. Wolter and M. Zakharyaschev) [PS]
- Real algebraic geometry and constraint databases (by Floris Geerts and Bart Kuijpers) [PDF]
- Mathematical morphology (by Isabelle Bloch, Henk Heijmans and Christian Ronse) [PDF]
- Spatial reasoning and ontology: parts, wholes, and locations (by Achille C. Varzi) [PDF]
モデル理論 [▲]
- 坪井明人，「2009年講義ノート： 数理論理学I」．[PDF]
- Anand Pillay, “Model theory,” Notices of the AMS, vol. 47, no. 11, 2000. [PDF]
- William Weiss and Cherie D’Mello, “Fundamentals of model theory.”
- Stephen G. Simpson, “Lecture notes: Model Theory.” [PDF]
- Jaap van Oosten, “Lecture notes: Model Theory.” [PS]
- J. Donald Monk, “Lecture notes: Math 6000, Model Theory.”
- Thomas Scanlon, “Lecture notes for Math 225a.” [PDF]
- Harold Simmons, An Introduction to Good Old Fashioned Model Theory. [PDF]
- Martin Ziegler, „Vorlesung über Modelltheorie I.“ [PDF]
- Georg Kreisel and Jean-Louis Krivine, Elements of Mathematical Logic (Model Theory), North-Holland, 1967. [PDF]
- Jon Barwise and Solomon Feferman (eds.), Model-Theoretic Logics, Springer, 1985.
- David Marker, Margit Messmer and Anand Pillay, Model Theory of Fields, Springer, 1996.
安定性理論 [▲]
- Lou van den Dries, “Introduction to model-theoretic stability.” [DVI]
- Boris Zilber, “Elements of geometric stability theory.” [PDF]
- Martin Ziegler, „Vorlesung über Modelltheorie II.“ [PDF]
- Martin Ziegler, „Stabilitätstheorie.“ [PDF]
- John T. Baldwin, Fundamentals of Stability Theory, Springer, 1988.
- Steve Buechler, Essential Stability Theory, Springer, 1996.
無限論理 [▲]
- David Marker, “Lecture notes: A Primer on Infinitary Logic.”
- Sections 1-2 [PDF]
- Section 3 [PDF]
- Section 4 [PDF]
- Section 5 [PDF]
- H. Jerome Keisler and Julia F. Knight, “Barwise: infinitary logic and admissible sets,” Bulletin of Symbolic Logic, vol. 10, no. 1, 2004. [PS]
計算可能性理論および再帰理論 [▲]
- 照井一成，「再帰的関数論」．[PDF]
- Lou van den Dries, “Recusion theory notes.” [PS]
- Dag Normann, “Lecture notes: Mathematical Logic II.” [PDF]
- Justus Diller, Berechenbarkeitstheorie.
- Martin Ziegler, „Rekursionstheorie.“ [PDF]
- Joseph R. Shoenfield, Recursion Theory, Springer, 1993.
- Edward R. Griffor (ed.) Handbook of Computability Theory, North-Holland, 1999.
- Local degree theory (by S. Barry Cooper) [PS]
- The recursively enumerable degrees (by Richard A. Shore) [PDF]
- Ordinal recursion theory (by C. T. Chong and Sy D. Friedman) [PDF]
- Recursion on abstract structures (by Peter G. Hinman) [PDF]
- Classifying recursive functions (by Helmut Schwichtenberg) [PS]
- Computation models and function algebras (by Peter Clote) [PDF]
- Stephen G. Simpson, “Lecture notes: Degrees of Unsolvability.” [PDF]
- Manuel Lerman, Degrees of Unsolvability: Local and Global Theory, Springer, 1983.
- Stephen G. Simpson, “Lecture notes: Topics in Logic and Foundations, Spring 2005.” [PDF]
- Peter G. Hinman, Recursion-Theoretic Hierarchies, Springer, 1978.
- Jon Barwise, Admissible Sets and Structures: An Approach to Definability Theory, Springer, 1975.
- Gerald E. Sacks, Higher Recursion Theory, Springer, 1990.
- Marian B. Pour-El and J. Ian Richards, Computability in Analysis and Physics, Springer, 1989.
集合論 [▲]
- 加茂静夫，「集合と論理」．[PDF]
- 新井敏康，「数学基礎論・数理科学続論D」．
- Boris Zilber, “Lecture notes: Axiomatic Set Theory.” [PDF]
- J. Donald Monk, “Lecture notes: Math 8714, Topics in Logic.”
- J. Donald Monk, “Lecture notes: Math 6730, Advanced Set Theory.”
- John R. Steel, “Set theory” in Encyclopedia of Life Support Systems. [PS]
- Wolfram Pohlers, Mengenlehre.
- Martin Ziegler, „Vorlesung über Mengenlehre.“ [PDF]
- Patrick Dehornoy, « Logique et théorie des ensembles », Notes de cours, FIMFA ENS, version 2006-2007.
- Chapitre 1 : Le type ensemble [PDF]
- Chapitre 2 : Les ordinaux [PDF]
- Chapitre 3 : Le système ZF [PDF]
- Chapitre 4 : L’axiome du choix [PDF]
- Chapitre 5 : Les cardinaux [PDF]
- Chapitre 6 : Logique propositionnelle [PDF]
- Chapitre 7 : Logique du premier ordre [PDF]
- Chapitre 8 : Théorèmes de limitation [PDF]
- Chapitre 9 : Modèles de ZFC [PDF]
- Chapitre 10 : Les ensembles constructibles [PDF]
- Joan Bagaria and Neus Castells (eds.) Set Theory: Centre de Recerca Matemàtica Barcelona, 2003-2004, Birkhäuser, 2006.
- An Ω-logic primer (by Joan Bagaria, Neus Castells and Paul B. Larson) [PDF]
- Real-valued measurable cardinals and well-orderings of the reals (by Andrés Eduardo Caicedo) [PDF]
- Complexity of sets and binary relations in continuum theory: a survey (by Alberto Marcone) [PDF]
- Weak systems of Gandy, Jensen and Devlin (by A. R. D. Mathias) [PDF]
- Some new directions in infinite-combinatorial topology (by Boaz Tsaban)
- Matthew Foreman and Akihiro Kanamori (eds.), Handbook of Set Theory, Springer, 2010.
- Stationary sets (by Thomas Jech) [PDF]
- Partition relations (by András Hajnal and Jean A. Larson) [PDF]
- Coherent sequences (by Stevo Todorčević) [PDF]
- Borel equivalence relations (by Greg Hjorth) [DVI]
- Proper forcing (by Uri Abraham) [PDF]
- Combinatorial cardinal characteristics of the continuum (by Andreas Blass) [PDF]
- Invariants of measure and category (by Tomek Bartoszynski)
- Constructibility and class forcing (by Sy D. Friedman) [PDF]
- Fine structure (by Ralf Schindler and Martin Zeman) [PDF]
- Σ* fine structure (by Philip D. Welch) [PS]
- Elementary embeddings and algebra (by Patrick Dehornoy) [PDF]
- Iterated forcing and elementary embeddings (by James Cummings) [PDF]
- Cardinal arithmetic (by Uri Abraham and Menachem Magidor) [DVI]
- Prikry-type forcings (by Moti Gitik) [PDF]
- Beginning inner model theory (by William J. Mitchell) [PDF]
- The covering lemma (by William J. Mitchell) [PDF]
- An outline of inner model theory (by John R. Steel) [PDF]
- A core model toolbox and guide (by Ernest Schimmerling) [PDF]
- Structural consequences of AD (by Steve Jackson) [PDF]
- Determinacy in L(R) (by Itay Neeman) [PDF]
- Large cardinals from determinacy (by Peter Koellner and W. Hugh Woodin) [PDF]
pcf理論 [▲]
- Menachem Kojman, “The A,B,C of pcf: a companion to pcf theory, part I.”
- Thomas Jech, “Singular cardinals and the pcf theory,” Bulletin of Symbolic Logic, vol.1, no.4, 1995. [PDF]
- J. Donald Monk, “Basic pcf theory.” [PDF]
記述集合論 [▲]
実数の集合論 [▲]
選択公理 [▲]
- John L. Bell, The Axiom of Choice, College Publications, 2009. [PDF]
強制法と内部モデル [▲]
- 渕野昌，「強制法入門： Aufforderung zur Erzwingungsmethode (Forcing)」．[PDF]
- Thomas Jech, “What is ... forcing?” Notices of the AMS, vol. 55, no. 6, 2008. [PDF]
- Martin Ziegler, „Forcingerweiterungen.“ [PDF]
- Saharon Shelah, Proper and Improper Forcing, 2nd ed., Springer, 1998.
- Keith J. Devlin, Constructibility, Springer, 1984.
- William J. Mitchell and John R. Steel, Fine Structure and Iteration Trees, Springer, 1994.
- Benedikt Löwe and John R. Steel, “An introduction to core model theory” in S. Barry Cooper and John K. Truss (eds.), Sets and Proofs, Cambridge University Press, 1999. [PDF]
- John R. Steel, The Core Model Iterability Problem, Springer, 1996.
連続体仮説 [▲]
- 渕野昌，「連続体仮説とゲーデルの集合論的宇宙」．[PDF]
- 依岡輝幸，「強制公理とΩ-論理」．
- Peter Koellner, “The Continuum Hypothesis” in Stanford Encyclopedia of Philosophy. [PDF]
- W. Hugh Woodin, “The Continuum Hypothesis, part I,” Notices of the AMS, vol. 48, no. 6, 2001. [PDF]
- W. Hugh Woodin, “The Continuum Hypothesis, part II,” Notices of the AMS, vol. 48, no. 7, 2001. [PDF]
- Patrick Dehornoy, “Recent progress on the Continuum Hypothesis (after Woodin).” [PDF]
NF [▲]
- M. Randall Holmes, Elementary Set Theory with a Universal Set, Cahiers du Centre de logique, vol. 10, Academia, 1998. [PDF]
証明論と構成的数学 [▲]
- 新井敏康，「Cut eliminationを中心とした証明論入門」．[PDF]
- Toshiyasu Arai, “Introduction to proof theoty.” [PDF]
- William W. Tait, “Lectures on Proof Theory.” [PDF]
- Herman Ruge Jervell, “A course in proof theory.” [PS]
- Samuel R. Buss, “Lectures on proof theory,” Technical Report SOCS-96.1, School of Computer Science, McGill University, 1996.
- Wolfram Pohlers, Infinitary Proof Theory.
- Wilfried Buchholz, „Beweistheorie.“ [PS]
- Samuel R. Buss (ed.), Handbook of Proof Theory, North-Holland, 1998.
- An introduction to proof theory (by Samuel R. Buss)
- First-order proof theory of arithmetic (by Samuel R. Buss)
- Gödel’s functional (“Dialctica”) interpretation (by Jeremy Avigad and Solomon Feferman) [PDF]
- The logic of provability (by Giorgi Japaridze and Dick de Jongh) [PDF]
- The lengths of proofs (by Pavel Pudlák) [PDF]
- A proof-theoretic framework for logic programming (by Gerhard Jäger and Robert Stärk) [PDF]
- Greg Restall, Proof Theory and Philosophy.
- Jan von Plato, “Natural deduction: some recent developments.” [PDF]
- Sara Negri, “Five lectures on proof analysis.” [PDF]
- Jean-Yves Girard, Yves Lafont and Paul Taylor, Proofs and Types, Cambridge University Press, 1989.
- Hiroakira Ono, “Proof-theoretic methods for nonclassical logic: an introduction” in M. Takahashi, M. Okada and M. Dezani-Ciancaglini (eds.), Theories of Types and Proofs, MSJ Memoire 2, Mathematical Society of Japan, 1998. [PS]
順序数解析 [▲]
- Toshiyasu Arai, “Introduction to ordinal analyses.” [PDF]
- Michael Rathjen, “The realm of ordinal analysis” in S. Barry Cooper and John K. Truss (eds.), Sets and Proofs, Cambridge University Press, 1999. [PS]
- Michael Rathjen, “The art of ordinal analysis” in M. Sanz-Solé, J. Soria, J. L. Varona and J. Verdera (eds.), Proceedings of the International Congress of Mathematicians, vol. 2, European Mathematical Society, 2006. [PDF]
算術の体系と不完全性 [▲]
- Jaap van Oosten, “Introduction to Peano arithmetic: Gödel incompleteness and nonstandard models.” [PS]
- 照井一成，「『数学』を数学的に考える」．[PDF]
- 黒田覚，「限定算術の新展開」．[PDF]
- Edward Nelson, Predicative Arithmetic, Princeton University Press, 1986. [PDF]
- Samuel R. Buss, Bounded Arithmetic, Bibliopolis, 1986.
- Petr Hájek and Pavel Pudlák, Metamathematics of First-Order Arithmetic, Springer, 1998.
- Per Lindström, Aspects of Incompleteness, Springer, 1997.
証明可能性論理 [▲]
- Sergei N. Artemov and Lev D. Beklemishev, “Provability logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 13, Kluwer, 2004. [PDF]
線形論理 [▲]
- 照井一成，「線形論理の誕生」．[PDF]
- Jean-Yves Girard, “Linear logic,” Theoretical Computer Science, vol. 50, no. 1, 1987. [PDF]
- A. S. Troelstra, Lectures on Linear Logic, CSLI, 1992.
構成的数学 [▲]
- Joan Moschovakis, “Notes on the foundations of constructive mathematics.” [PDF]
代数的論理と圏論 [▲]
- 小野寛晰，「代数的視点からの論理へのアプローチ」．[PDF]
- Hajnal Andréka, István Németi and Ildikó Sain, “Algebraic logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 2, Kluwer, 2001. [PDF]
- Hajnal Andréka, Ágnes Kurucz, István Németi and Ildikó Sain, “Applying algebraic logic: a general methodology.” [PDF]
- Hajnal Andréka, Miklós Ferenczi and István Németi (eds.), Cylindric-like Algebras and Algebraic Logic, Springer, 2013.
- Reducing first-order logic to Df3, free algebras (by Hajnal Andréka and István Németi) [PDF]
- Varieties of two-dimensional cylindric algebras (by Nick Bezhanishvili) [PDF]
- Representable cylindric algebras and many-dimensional modal logics (by Agi Kurucz) [PDF]
- Cylindric modal logic (by Yde Venema) [PDF]
- CRS and guarded logics: a fruitful contact (by Johan van Benthem) [PDF]
- Cylindric set algebras and IF logic (by Allen L. Mann) [PDF]
ブール代数 [▲]
- J. Donald Monk, “A brief introduction to Boolean algebras.” [PS]
普遍代数 [▲]
- K. Meinke and J. V. Tucker, “Universal algebra” in S. Abramsky, D. M. Gabbay and T. S. E. Maibaum (eds.), Handbook of Logic in Compute Science, vol. 1, Oxford University Press, 1992. [PS]
- Stanley N. Burris and H. P. Sankappanavar, A Course in Universal Algebra: The Millennium Edition.
量子論理 [▲]
- Maria Luisa Dalla Chiara and Roberto Giuntini, “Quantum logic” in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd ed., vol. 6, Kluwer, 2002.
- Dov M. Gabbay, Kurt Engesser and Daniel Lehmann, A New Approach to Quantum Logic, College Publications, forthcoming. [PDF]
- Kurt Engesser, Dov M. Gabbay and Daniel Lehmann (eds.), Handbook of Quantum Logic and Quantum Structures: Quantum Logic, Elsevier, 2008.
- Is quantum logic a logic? (by Mladen Pavičić and Norman D. Megill)
- Is logic empirical? (by Guido Bacciagaluppi)
- Quantum axiomatics (by Diederik Aerts) [PDF]
- Categorical quantum mechanics (by Samson Abramsky and Bob Coecke)
- Extending classical logic for reasoning about quantum systems (by R. Chadha, P. Mateus, A. Sernadas and C. Sernadas) [PDF]
- Contexts in quantum, classical and partition logic (by Karl Svozil) [PDF]
- A quantum logic of down below (by Peter D. Bruza, Dominic Widdows and John H. Woods) [PDF]
- 小澤正直，「量子集合論と量子力学の解釈問題」．
- 小澤正直，「論理・集合・実数・物理・測定：量子集合論と量子力学の観測問題」．
圏論 [▲]
- Steve Awodey, Category Theory, Oxford University Press, 2006.
- Tom Leinster, Basic Category Theory, Cambridge University Press, 2014.
- Jaap van Oosten, “Lecture notes: Basic Category Theory.” [PDF]
- Andrea Schalk and Harold Simmons, An Introduction to Category Theory in Four Easy Movements. [PDF]
- Ieke Moerdijk and Jaap van Oosten, “Lecture notes: Topos Theory.” [PDF]
- Michael Barr and Charles Wells, Toposes, Triples and Theories, Springer, 1983.
- Andrea Asperti and Giuseppe Longo, Categories, Types and Structures: Category Theory for the Working Computer Scientist, MIT Press, 1991. [PDF]
- John L. Bell, Notes on Toposes and Local Set Theories. [PDF]
歴史 [▲]
- Solomon Feferman, “The development of programs for the foundations of mathematics in the first third of the 20th century.” [PDF]
- Solomon Feferman, “Highlights in proof theory” in V. F. Hendricks, S. A. Pedersen and K. F. Jørgensen (eds.), Proof Theory: History and Philosophical Significance, Kluwer, 2000. [PDF]
- Solomon Feferman, “Proof theory since 1960” in D. M. Borchert (ed.), The Encyclopedia of Philosophy. Supplement, Macmillan, 1996. [PDF]
- Wilfrid Hodges, “Model theory.” [PDF]
- Dov Gabbay and John Woods (eds), Handbook of the History of Logic, 11 vols., Elsevier, 2004-.
- Leibniz’s logic (by Wolfgang Lenzen) [PDF]
- Frege’s logic (by Peter Sullivan) [PDF]
- The logic of Brouwer and Heyting (by Joan Moschovakis) [PDF]
- The logic of Church and Curry (by Jonathan P. Seldin) [PDF]
- Set theory from Cantor to Cohen (by Akihiro Kanamori) [PDF]
- Singular cardinals: from Hausdorff’s gaps to Shelah’s pcf theory (by Menachem Kojman) [PDF]
- The history of categorical logic: 1963-1977 (by Jean-Pierre Marquis and Gonzalo Reyes) [PDF]
- Mathematical modal logic: a view of its evolution (by Robert Goldblatt) [PDF]
- Relevant and substructural logics (by Greg Restall)
- The Gamut of dynamic logics (by Martin Stokhof and Jan van Eijck) [PDF]
- Situation theory and situation semantics (by Keith Devlin) [PDF]
- Fuzzy-set based logics: an history-oriented presentation of their main developments (by D. Dubois, F. Esteva, L. Godo and H. Prade) [PDF]
- An explorer upon untrodden ground: Peirce on abduction (by Stathis Psillos) [PDF]
- Hempel and the paradox of confirmation (by Jan Sprenger) [PDF]
- Goodman and the demise of the syntactic and semantic models (by Robert Schwartz) [PDF]
- Varieties of Bayesianism (by Jonathan Weisberg) [PDF]
- Inductive logic and statistics (by Jan-Willem Romeijn) [PDF]
