Joan Rand Moschovakis

Guest of the UCLA Mathematics Department   

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Education

• Ph.D., Mathematics, University of Wisconsin, 1965
• M.S., Mathematics, University of Wisconsin, 1961
• BA, Mathematics, UC Berkeley, Summa Cum Laude, 1959

Honors

• Woodrow Wilson and NSF Graduate Fellowships
• Lindstrom Lecturer, 2014

Research Interests

• Foundations of intuitionistic arithmetic and analysis: the mathematics of natural numbers and infinitely proceeding sequences  
• Intuitionistic interpretations of classical mathematics
• Classical interpretations of intuitionistic mathematics
• Admissible rules of formal systems based on intuitionistic logic
• History and philosophy of intuitionistic logic and mathematics

Notes In Progress

• Notes on the Foundations of Constructive Mathematics, in progress  (December 2006).    newnotes.ps,  newnotes.pdf

Online Publications

• Calibrating the negative interpretation, expanded version of an extended abstract for a contributed talk at the 12th Panhellenic Logic Symposium (2019). arXiv:2101.10313[math.LO].
• (with Garyfallia Vafeiadou), : Intuitionistic mathematics and logic.   arXiv:2003.01935[math.LO].
• Intuitionistic Logic, revised 2022, Stanford On-Line Encyclopedia of Philosophy (Summer 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.).    logic-intuitionistic.
• Note on Π⁰_n+1-LEM, Σ⁰_n+1-LEM and Σ⁰_n+1-DNE , originally in Proceedings of 5th Panhellenic Logic Symposium (2005), 99-104. arXiv:1807.10472[math.LO].

Slides of Invited Lectures

• Brouwer's notion of choice sequence and its descendants, Infinity and Intensionality Colloquium, Univ. of Oslo, December 7, 2022    OsloCShandout.pdf
• Minimum classical extensions of constructive theories, CiE 2021: Connecting with Computability, July 5, 2021    CiE2021handout.pdf
• Constructive significance of the negative interpretation of classical analysis, Special session on proof theory, ASL 2020 annual meeting (cancelled because of the coronavirus)   irvine2020handout.pdf
• Patterns and principles in Troelstra's metamathematical work, Memorial event for A. S. Troelstra, Amsterdam, March 2020   troelstramemorialhandout.pdf
• A logical look at Kripke's idea of choice sequence, 46th annual Society for Exact Philosophy meeting, Storrs, CT, May 2018   logicalKripkelookhandout.pdf
• Brouwer, Kleene, Kripke and the end of time, ASL 2017 Spring meeting (with APA Pacific Division)   seattle2017handout.pdf
• Markov's Principle, Markov's Rule and the notion of constructive proof, Computation and Proof: Selected themes from the research of G. Kreisel, IHST, Paris, 9-10 June, 2016   paris2016handout.pdf
• Choice sequences and their uses, Workshop on Spreads and Choice Sequences, Mittag-Leffler Institute, Stockholm, Sweden, June 8-10, 2015   stockholm2015handout.pdf
• Intuitionistic analysis, forward and backward, Public Lindstrom Lecture, Gothenburg, Sweden, October 23, 2014   publiclindstromhandout.pdf
• Now under construction: intuitionistic reverse analysis, Technical Lindstrom Lecture, Gothenburg, Sweden, October 24, 2014   technicallindstromhandout.pdf
• Embedding the constructive and the classical in the intuitionistic continuum, Proof, Truth and Computation, Fraueninsel, Chiemsee, July 24, 2014   chiemsee2014handout.pdf
• Embedding the classical in the intuitionistic continuum, UC Irvine, April 4, 2014   irvine2014handout.pdf
• Constructive taxonomy, Amsterdam, Heyting Day, September 7, 2012   amsterdamhandout.pdf
• Waltzing around Markov's Principle, Nijmegen, September 10, 2012   nijmegenhandout.pdf
• ``At Most One'' Constructively, Artemov 60th at CUNY, May 23-25, 2012   artemovhandout.pdf
• Models and interpretations of (intuitionistic) analysis, VIG at UCLA, February 4-6, 2011   vig2011handout.pdf
• Exercises in reverse constructive analysis (joint with Garyfallia Vafeiadou),Chiemsee, June 6-11, 2010   chiemseehandout.pdf
• Varieties of reverse constructive mathematics, CUNY Computational Logic Seminar, January 2008 (revised and expanded version of UCLA Logic Colloquium, April 2007)   reversehandout.pdf
• Unavoidable choice sequences, Oberwolfach Week in Proof Theory and Constructive Math, April 2008; also Conference for Fred and Ray, May 2008  unavoidablehandout.pdf
• Hierarchies in Intuitionistic Arithmetic, Gjuletchica, December 2002: bulg02sl.pdf,   bulg02sl.ps

Selected Publications and Preprints 

• Classical consequences of constructive systems, Phil. Trans. R. Soc. A 381:20220011 (2023).    Author's version, with typos corrected: classicalconsequences.pdf
• (with Garyfallia Vafeiadou): Minimum classical extensions of constructive theories, Connecting with Computability, Proceedings of CiE 2021, 353-362.    Authors' version: minclassext.pdf
• Markov's Principle, Markov's Rule and the notion of constructive proof, revised version of a chapter intended for a forthcoming book ``Intuitionism, Computation and Proof: Selected themes from the research of G. Kreisel,'' M. Antonutti Marfori and M. Petrolo, eds.    Preprint: MPandMRpreprint.pdf
• Markov's Principle and subsystems of intuitionistic analysis, Journal of Symbolic Logic 84 (2019), 870-876.   Preprint: MPandsubsystemspreprint.pdf
• (with Yiannis Moschovakis): Intuitionism and effective descriptive set theory, Indagationes Mathematicae, 2017.   Preprint: moschovakis-brouwer.pdf
• Intuitionistic analysis at the end of time, Bulletin of Symbolic Logic 23 (2017), 279-295.   Accurate preprint: endoftimepreprint.pdf
• A translation theorem for restricted R-formulas, IfCoLog Journal of Logics and their Applications, November 2016.   Preprint: translationtheoremtopost.pdf
• Iterated definability, lawless sequences and Brouwer's continuum, in ``Godel's Disjunction: The Scope and Limits of Mathematical Knowledge,'' ed. Philip Welch and Leon Horsten, Oxford University Press, 2016.   Preprint: bristoltopost.pdf
• Another Unique Weak K\"onig's Lemma, in ``Logic, Construction, Computation,'' U. Berger, H. Diener, P. Schuster, M. Seisenberger (Eds.), Ontos 2012.   Preprint: anotheruniqueWKL.pdf
• (with Garyfallia Vafeiadou): Some axioms for constructive analysis, Archive for Mathematical Logic, 2012.   Preprint: someaxiomstopost.pdf
• Unavoidable sequences in constructive analysis, Mathematical Logic Quarterly, 2010.  Preprint: MLQnote10topost.pdf
• The Logic of Brouwer and Heyting, a chapter in ``Logic from Russell to Church,'' Volume 5 of the Handbook of the History of Logic, ed. Woods and Gabbay, Elsevier, 2009. Preprint:  logicofBandH.pdf,  logicofBandH.ps
• (with Garyfallia Vafeiadou, in Greek): Ta Enoratika Mathimatika kai i Logiki tous, Stigmes kai Diarkies, ed. D. Anapolitanos, Nefeli, 2009.  gvfjrmgr.pdf,   gvfjrmgr.ps
• (with Garyfallia Vafeiadou, English translation now on arXiv): Intuitionistic mathematics and logic.   gvfjrmeng.pdf,   gvfjrmeng.ps
• Note on Π⁰_n+1-LEM, Σ⁰_n+1-LEM and Σ⁰_n+1-DNE, Proceedings of 5th Panhellenic Logic Symposium (2005). pls5.ps,    pls5.pdf
• The effect of Markov's Principle on the intuitionistic continuum, Proceedings of Oberwolfach Proof Theory week (April 2005). markov.ps,    markov.pdf
• Notes on the Foundations of Constructive Mathematics, in progress  (December 2006).    newnotes.ps,  newnotes.pdf
• Classical and constructive hierarchies in extended intuitionistic analysis, Journal of Symbolic Logic 64 (2003), 1015-1043.   (In the proof of Lemma 5.5(c), on lines -9 and -12, four occurrences of "(w)_j - 1" should be replaced by "(w)_j - 2.")
• Analyzing realizability by Troelstra's methods, Annals of Pure and Applied Logic 114 (2002), 203-225
• A classical view of the intuitionistic continuum, Annals of Pure and Applied Logic, 1996.
• Corrected version of An intuitionistic theory of lawlike, choice and lawless sequences, in Logic Colloquium '90 (ASL Helsinki), LNL 2 (1991).   (The published version had a serious systematic error, which is corrected here.)   helsinkicorr.pdf,   helsinkicorr.ps
• Relative lawlessness in intuitionistic analysis, Journal of Symbolic Logic, 1987. 
• A topological interpretation of second-order intuitionistic arithmetic, Compositio Mathematica, 1973.  (The argument I gave there for x27.2 without free function variables is incorrect, as Scedrov pointed out soon afterward.  Krol later gave a correct argument for the schema without this restriction, using a more intricate topological model, and van Dalen showed by a counterexample that the restriction could not be removed for my model. )
• Can there be no nonrecursive functions?, Journal of Symbolic Logic, 1971.
• Disjunction and existence in formalized intuitionistic analysis, in ``Sets, Models and Recursion Theory,'' ed. J. Crossley, North-Holland, 1967. 

Professor Moschovakis is Emerita Professor of Mathematics, Occidental College. She has also taught in the Graduate Program in Logic and Algorithms at the University of Athens, Greece, where she enjoyed supervising the Master's Thesis and PhD dissertation of Garyfallia Vafeiadou and the Master's Thesis of Nikos Vaporis. 

Comments on and corrections to the Stanford Encyclopedia article on Intuitionistic Logic, and "Notes on the Foundations of Constructive Mathematics," will be very much appreciated.

Last Updated:  8/06/2023

E-mail: joan@math.ucla.edu  ,   joan.rand@gmail.com

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Guest, UCLA Mathematics Dept.