# Publications

## Books in preparation

*Apartness Spaces*(with Luminiţa Vîţă), graduate monograph.

## Refereed/invited articles

There follows a list of my research papers, grouped under the following headings:

Algebra; Apartness and uniform spaces; Approximation theory; Constructive mathematics‒general articles; Constructive mathematics and physics; Constructive reverse mathematics; Dirichlet problem; Economic theory; Extended reviews; Functional analysis; Locally convex spaces; Measure and integration; Metric and normed spaces; Miscellaneous constructive papers; Real and complex analysis; Set theory

### Algebra

- ‘On the derivation of x
^{n}in a ring’ (with Jeffrey Bergen), Proc. Amer. Math. Soc.**90**(1), 25–29, 1984. - ‘Prime and maximal ideals in constructive ring theory’, Comm. Algebra.
**29**(7), 2787–2803, 2001. - ‘The polydisk Nullstellensatz’ (with Ray Mines, Peter Schuster, and Fred Richman), Proc. Amer. Math. Soc.
**132**(7), 2133–2140, 2004. - ‘A simple constructive proof of Kronecker’s density theorem’ (with Peter Schuster), Elemente der Mathematik
**61**, 152–154, 2006.

### Apartness and uniform spaces

- ‘Characterising near continuity constructively’ (with Luminiţa Vîţă), Math. Logic Quart.
**27**(4), 535–538, 2001. - ‘Apartness as a relation between subsets’ (with Peter Schuster and Luminiţa Vîţă), in:
*Combinatorics, Computability and Logic*(Proceedings of DMTCS’01, Constanţa, Romania, 2–6 July 2001; C.S. Calude, M.J. Dinneen, S. Sburlan (eds.)), 203–214, DMTCS Series**17**, Springer–Verlag, London, 2001. - ‘Cauchy nets in the constructive theory of apartness spaces’ (with Luminiţa Vîţă), Scientiae Mathematicae Japonicae
**56**, 123–132, 2002. - ‘Apartness, topology, and uniformity: a constructive view’ (with Peter Schuster and Luminiţa Vîţă),
*Computability and Complexity in Analysis*(Proc. Dagstuhl Seminar 01461, 11–16 November 2001), Math. Log. Quart.**48,**Suppl. 1, 16–28, 2002. - ‘Apartness spaces—a progress report’, European Assoc. for Theoretical Computer Science Bull.
**81**, 2003. - ‘Apartness spaces as a framework for constructive topology’ (with Luminiţa Vîţă), Ann. Pure Appl. Logic.
**119**(1–3), 61–83, 2003. - ‘Strong versus uniform continuity: a constructive round’ (with Peter Schuster and Luminiţa Vîţă), Quaest. Math.
**26**, 171–190, 2003. - ‘A constructive theory of point–set nearness’ (with Luminiţa Vîţă),
*Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitization*(Proc. Dagstuhl Seminar 00231, 4-9 June 2000; R. Kopperman, M. Smyth, D. Spreen, eds.), Theoretical Computer Science**305**(1–3), 473–489, 2003. - ‘A proof–technique in uniform space theory’ (with Luminiţa Vîţă),
**68**(3), 795–802, 2003. (A corrigendum to this paper has been published in volume**69**(1), p.328, 2004.) - ‘Cauchy nets in uniform apartness spaces’ (with Luminiţa Vîţă), Revue Romaine
**48**(5–6), 467–474, 2003. - ‘Strong and uniform continuity—the uniform space case’ (with Luminiţa Vîţă), London Math. Soc. J. Computing & Math.
**6**, 326–334, 2003. - ‘Separatedness in constructive topology’ (with Luminiţa Vîţă), Documenta Mathematica
**8**, 567–576, 2003. - ‘More on Cauchy nets in apartness spaces’ (with Luminiţa Vîţă), Sci. Math. Japonicae
**9**, 375–380, 2004. - ‘A general constructive proof technique’ (with Luminiţa Vîţă), Elec. Notes in Theoretical Comp. Sci.
**120**, 31–43, 2005. - ‘Products in the category of apartness spaces’ (with Hajime Ishihara, Peter Schuster and Luminiţa Vîţă), Cahiers de Topologie et Géometrie Différentielle
**46**, 139–153, 2005. - ‘Strong continuity implies uniform sequential continuity’ (with Hajime Ishihara, Peter Schuster and Luminiţa Vîţă), Archive for Math. Logic
**44**(7), 887–895. - ‘A constructive treatment of Urysohn’s lemma in an apartness space’ (with Hannes Diener), Math. Logic Quarterly
**52**(5), 464–469, 2006. - ‘Pre-apartness structures on spaces of functions’ (with Luminiţa Vîţă), J. Complexity Theory (Special Issue, Proc. CCA 05 Kyoto)
- ‘Almost locatedness in uniform spaces’ (with Hajime Ishihara, Ray Mines, Fred Richman, Peter Schuster, and Luminiţa Vîţă), Czech. Math. J.
- ‘Journey into apartness space’ (with Luminiţa Vîţă), in:
*Logicism, Formalism, Intuitionism‒What has Become of Them?*(S. Lindström, E. Palmgren, K. Segerberg, and V. Stoltenberg-Hansen, eds) Synthese Library, Springer–Verlag, Berlin, to appear in 2008. - ‘Product a–frames and proximity’, Math. Logic Quaterly
**54**(1), 12–25, 2008. - ‘Proximal connectedness’ (with Luminiţa Vîţă), Fundamenta Informaticae
**83**(1-2), 25–34, 2008. - ‘Apartness, compactness and nearness’ (with Hajime Ishihara, Peter Schuster, and Luminiţa Vîţă), Theoretical Comp. Sci. (special issue of proceedings of Dagstuhl 2006 topology meeting, to appear.

### Approximation theory

- ‘On the foundations of best approximation theory’, J. Approx. Theory,
**28**(3), 273–292, 1980. - ‘A constructive development of Chebyshev approximation theory’, J. Approx. Theory
**30**(2), 99–120, 1981. - ‘A constructive analysis of the Remes algorithm’, J. Approx. Theory
**32**(4), 257–270, 1981. - ‘A constructive proximinality property of finite–dimensional linear spaces’, Rocky Mountain J. Math.
**11**(4), 491–497, 1981. - ‘Lipschitz constants and moduli of continuity for the Chebyshev projection’, Proc. Amer. Math. Soc.
**85**(4), 557–561, 1982. - ‘Recent progress in constructive approximation theory’, in
*The L.E.J. Brouwer Centenary Symposium*(A.S. Troelstra and D. van Dalen, eds.), North–Holland, Amsterdam, 41–50, 1982. - ‘Approximate interpolation by functions in a Haar space’, J. Approx. Theory
**57**(1), 35–39, 1989. - ‘Constructing best approximations on a Jordan curve’ (with Wang Yuchuan), J. Approx. Theory
**94**(2), 222–234, 1998. - ‘Continuity and Lipschitz constants for projections’, J. Logic and Alg. programming, special issue for Dieter Spreen’s 60th birthday.

### Constructive mathematics‒general articles

- ‘What is constructive mathematics?’ (with Ray Mines), Math. Intelligencer
**6**(4), 32–38, 1985. - ‘Constructive Mathematics’, in
*Stanford Encyclopedia of Philosophy*(ISSN 1095–5054). - ‘Paradise lost, or Paradise regained?’ (with Luminiţa Dediu), EATCS Bulletin
**63**, 141–152, October 1997. - ‘Constructive truth in practice’, in
*Truth in Mathematics*(Proceedings of Conference held at Mussomeli, Sicily, 13–21 September 1995; H.G. Dales and G. Oliveri, eds), 53–69, Clarendon Press, Oxford, 1998. - ‘Constructive mathematics, in theory and programming practice’ (with Steve Reeves), Philosophia Mathematica
**7**(1), 65–104, 1999. - ‘Constructive mathematics: a foundation for computable analysis’, Theoretical Computer Science
**219**(1–2), 95-109, 1999. - ‘Constructivity in mathematics’, Cubo (Math. Journal of Universidad de la Frontera, Chile)
**6**(1), 209–258, 2004. - ‘Errett Bishop’, in:
*From Sets and**Types to Topology and Analysis*(L. Crosilla and P. Schuster, eds), vii–ix, Oxford Logic Guides, Clarendon Press, Oxford, 2005. - ‘Church’s thesis and Bishop.s constructivism’, in:
*Church’s Thesis After 70 Years*(Adam Olszewski, ed.), 58–65, Ontos Verlag, Berlin, 2006. - ‘Philosophy of mathematics: five questions’ in
*Philosophy of mathematics: five questions*(V.F. Hendricks and H. Leitgeb, eds), 45–49, New York, London: Automatic Press/VIP, 2007.

### Constructive mathematics and physics

- ‘Towards a constructive foundation for quantum mechanics’, in
*Constructive Mathematics*(F. Richman, ed.), Springer Lecture Notes in Math.**873**, 260–273, 1981. - ‘Constructive mathematics and unbounded operators—a reply to Hellman’, J. Philosophical Logic
**24**, 549–561, 1995. - ‘Can constructive mathematics be applied in physics?’, J. Philosophical Logic
**28**(5), 439-453, 1999. - ‘A constructive proof of Gleason’s theorem’ (Fred Richman and Douglas Bridges), Journal of Functional Analysis
**162**, 287-312, 1999. - ‘Constructive mathematics and quantum physics’ (with Karl Svozil), Int. J. Theor. Physics
**39**, 501-513 (2000).

### Constructive reverse mathematics

- ‘The fan theorem and unique existence of maxima’ (with Josef Berger and Peter Schuster), J. Symbolic Logic
**71**(2), 713–720, 2006. - ‘A bizarre property equivalent to the Π–fan theorem’ (with Josef Berger), Logic Journal of IGPL, Advance Access published online, 19 August 2006.
- ‘A fan–theoretic equivalent of the antithesis of Specker’s theorem’ (with Josef Berger), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math., N.S.),
**18**(20< 195–202, 2007. - ‘The pseudocompactness of [0, 1] is equivalent to the uniform continuity theorem’ (with Hannes Diener), J. Symbolic Logic
**72**(4), 1379–1383, 2008. - ‘The anti-Specker property, a Heine–Borel property, and uniform continuity’ (with Josef Berger), Archive for Math. Logic
**46**(7–8), 583–592, 2008. - ‘Continuity properties of preference relations’ (with Marian Baroni), Elec. Notes in Theor. Comp. Sci.
**202**, 19–25, 2008. - ‘Uniform continuity properties of preference relations’, Notre Dame Journal of Formal Logic
**49**(1), 97–106, 2008. - ‘A reverse look at Brouwer’s fan theorem’, Proc. Conference
*Cent Ans de I’Intuitionnisme*(Cerisy, Normandy, June 2006).

### Dirichlet problem

- ‘Constructing cutoff functions’ (with Wang Yuchuan), New Zealand J. Math.
**26**, 25–30, 1997. - ‘Constructive aspects of the Dirichlet problem’ (with Wang Yuchuan), J. Universal Comp. Sci.
**3**(11), 1148–1161, 1997. - ‘Weak solutions of the Dirichlet Problem and the Locatedness of ’ (with Wang Yuchuan), New Zealand J. Math.
**28**(1), 1–5, 1998. - ‘Constructive weak solutions of the Dirichlet Problem’ (with Wang Yuchuan), J. London Math. Soc.
**57**(3), 655–667 (Officially the June 1998 volume, but did not appear until January 1999).

### Economic theory

See also under *Constructive reverse mathematics*.

- ‘Preference and utility—a constructive development’, J. Math. Economics
**9**, 165–185, 1982. - ‘A numerical representation of preferences with intransitive indifference’, J. Math. Economics
**11**, 25–42, 1983. - ‘Numerical representation of intransitive preferences on a countable set’, J. Economic Theory
**30**, 213–217, 1983. - ‘Representing interval orders by a single real–valued function’, J. Economic Theory
**36**(1), 149–155, 1985. - ‘Numerical representation of interval orders on a topological space’, J. Economic Theory
**38**(1), 160–166, 1986. - ‘The Euclidean distance construction of order homomorphisms’, Math. Social Sciences
**15**(2), 179–188, 1988. - ‘The constructive theory of preference orderings on a locally compact space’, Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.)
**92**(2), 141–165, 1989. - ‘Preference, indifference, and Markov’s principle’, Math. Social Sciences
**20**, 131–146, 1990. - ‘Order isomorphisms: a constructive measure–theoretic view’, in
*Mathematical Logic: Proceedings of Heyting ’88 Conference in Logic*(P.P. Petkov, ed.), 243–255, Plenum Publishing Corp., New York, 1990. - ‘The constructive inequivalence of various notions of preference ordering’, Math. Soc. Sciences
**21**, 169–176, 1991. - ‘A recursive counterexample to Debreu’s theorem on the existence of a utility function’ (with Fred Richman), Math. Soc. Sciences
**21**, 179–182, 1991. - ‘The construction of a continuous demand function for uniformly rotund preferences’, J. Math. Economics
**21**, 217–227, 1992. - ‘The constructive theory of preference orderings on a locally compact space II’, Math. Social Sciences
**27**, 1–9, 1994. - ‘Constructive methods in mathematical economics’, in
*Mathematical Utility Theory*, J. Econ. (Zeitschrift für Nationalökonomie), Suppl.**8**, 1–21, 1999.

### Extended reviews

The following extended reviews were commissioned.

*A Course in Constructive Algebra*(by R. Mines, F. Richman, and W. Ruitenburg), Bull. American Math. Soc.**20**(1), 127–132, 1989.*Theories of Computational Complexity*(by C.S. Calude), Kybernetes**19**(3), 33–36, 1990.*Computability in Analysis and Physics*(by M.B. Pour–El and J.A. Richards), Bull. Amer. Math. Soc.**24**(1), 216–228, 1991.*Utility Maximization, Choice and Preference*(F. Aleskerov, D. Bouyssou, and B. Monjardet), to appear in SIAM Review.

### Functional analysis

- ‘On weak operator compactness of the unit ball of ’, Zeit. math. Logik Grundlagen Math.
**24**, 493–494, 1978. - ‘A constructive look at positive linear functionals on ’, Pacific J. Math.
**95**(1), 11–25, 1981. - ‘Operator ranges, integrable sets, and the functional calculus’, Houston J. Math.
**11**(1), 31–44, 1985. - ‘A constructive treatment of open and unopen mapping theorems’ (with W. Julian and R. Mines), Zeit. math. Logik Grundlagen Math.
**35**, 29–43, 1989. - ‘Locating the range of an operator on a Hilbert space’ (with Hajime Ishihara), Bull. London Math. Soc.
**24**, 599–605, 1992. - ‘Absolute continuity and the uniqueness of the constructive functional calculus’ (with Hajime Ishihara), Math. Logic Quarterly
**40**, 519–527, 1994. - ‘Spectra of selfadjoint operators in constructive analysis’ (with Hajime Ishihara), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.)
**7**(1), 11–36, 1996. - ‘Constructing ultraweakly continuous linear functionals on ’ (with Nicholas Dudley Ward), Proc. American Math. Soc.
**126**(11), 3347–3353, 1998. - ‘A definitive constructive open mapping theorem?’ (with Hajime Ishihara), Math. Logic Quarterly
**44**, 545–552, 1998. - ‘Weak-operator continuity and the existence of adjoints’ (with Luminiţa Dediu), Math. Logic Quarterly
**45**(2), 203–206, 1999. - ‘The weak–operator sequential continuity of left multiplication’ (with Luminiţa Dediu), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.).
**11**(1), 39–42, 2000. - ‘A constructive analysis of a proof of that the numerical range is convex’ (with Robin Havea), London Math. Soc. Journal of Mathematics and Computation
**3**, 191–206, 2000. - ‘Constructive methods in Banach algebra theory’, Math. Japonica
**52**(1), 145–161, 2000. - ‘Adjoints, absolute values, and polar decompositions’ (with Fred Richman and Peter Schuster), J. Operator Theory
**44**, 243–254, 2000. - ‘Constructing extensions of ultraweakly continuous linear functionals’ (with Luminiţa Vîţă), J. Functional Analysis
**178**(2), 421–434, 2000. - ‘Constructive closed range and open mapping theorems’ (with Hajime Ishihara), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.)
**11**(4), 509–516, 2001. - ‘A constructive version of the spectral mapping theorem’ (with Robin Havea), Math. Logic Quarterly
**47**(3), 299-304, 2001. - ‘Constructive unbounded operators’ (with Hajime Ishihara), in:
*Reuniting the Antipodes—Constructive and Nonstandard Views of the Continuum*(Berger, Ulrich, Horst Osswald, and Peter Schuster, editors), 25–37, Proceedings of the Symposion in San Servolo/Venice, Italy, May 17-22, 1999, Synthèse Library, Kluwer Academic Publishers, Dordrecht, December 2001. - ‘Trace-class operators’ (with Fred Richman and Peter Schuster), Houston J. Math.
**28**, 565–583, 2002. - ‘Locating the range of an operator with an adjoint’ (with Hajime Ishihara and Bas Spitters), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) N.S.,
**11**(3), 1–8, 2003. - ‘Approximating the numerical range in a Banach algebra’ (with Robin Havea), in:
*From Sets and Types to Topology and Analysis*(L. Crosilla and P. Schuster, eds), 293–303, Oxford Logic Guides, Clarendon Press, Oxford, 2005. - ‘Constructive Banach algebra theory and the Nullstellensatz.’ (with Robin Havea and Peter Schuster), Publ. Math. Debrecen
**69**(1–2), 171–184, 2006. - ‘Ideals in constructive Banach algebra theory’ (with Robin Havea and Peter Schuster), J. Complexity
**22**, 729–737, 2006. - ‘Powers of a Hermitian element’ (with Robin Havea), New Zealand J. Math.
**36**, 1–10, 2007.

### Locally convex spaces

- ‘Constructive notes on uniform and locally convex spaces’ (with Luminiţa Dediu), in Proceedings of 12th International Symposium, FCT’99 Iasi, Romania, Springer Lecture Notes in Computer Science
**1684**, 195–203, 1999. - ‘The constructive uniqueness of the locally convex topology on ’ (with Luminiţa Vîţă), in:
*From Sets and Types to Topology and Analysis*(L. Crosilla and P. Schuster, eds), 304–315, Oxford Logic Guides, Clarendon Press, Oxford, 2005.

### Measure and integration

- ‘The constructive Radon–Nikodým theorem’, Pacific J. Math.
**70**(1), 51–65, 1977. - ‘On the constructive convergence of series of independent functions’, Zeit. math. Logik Grundlagen Math.
**25**, 93–96, 1979. - ‘Locatedness, convexity, and Lebesgue measurability’, Quart. J. Math. Oxford (2)
**39**, 411–421, 1988. - ‘On the Lebesgue measurability of continuous functions in constructive analysis’ (with Osvald Demuth), Bull. Amer. Math. Soc.
**24**(2), 259–276, 1991. - ‘Colocatedness and Lebesgue interability’ in:
*Computation and Logic in the Real World*(proc. 3rd Conference on Computability in Europe, Siena, 2007; S.B. Cooper, L. Löwe, A. Sorbi, eds), Lecture Notes in Computer Science**4497**, 98–104, Springer–Verlag, Berlin–Heidelberg, 2007.

### Metric and normed spaces

- ‘Some notes on continuity in constructive analysis’, Bull. London Math. Soc.
**8**, 179–182, 1976. - ‘A constructive look at orthonormal bases in Hilbert space’, Amer. Math. Monthly,
**84**(3), 189–191, 1977. - ‘On the connectivity of convex sets’, Bull. London Math. Soc.
**10**, 86–90, 1978. - ‘More on the connectivity of convex sets’, Proc. Amer. Math. Soc.
**68**(2), 214–216, 1978. - ‘On continuous mappings between locally compact metric spaces’, Bull. London Math. Soc.
**10**, 201–208, 1978. - ‘A criterion for compactness in metric spaces?’, Zeit. math. Logik Grundlagen Math.
**25**, 97–98, 1979. - ‘Connectivity properties of metric spaces’, Pacific J. Math.
**80**(2), 325–333, 1979. - ‘Compactly generated Banach spaces’ (with F. Richman, A. Calder, W. Julian, and R. Mines), Arch. Math.
**36**, 239–243, 1981. - ‘Locating metric complements in ’ (with A. Calder, W. Julian, R. Mines, and F. Richman), in
*Constructive Mathematics*(F. Richman, ed.), Springer Lecture Notes in Math.**873**, 241–249, 1981. - ‘Bounded linear mappings of finite rank’ (with A. Calder, W. Julian, R. Mines, and F. Richman), J. Functional Anal.
**43**(2), 143–148, 1981. - ‘Linear mappings are fairly well–behaved’ (with Hajime Ishihara), Arch. Math.
**54**, 558–562, 1990. - ‘Extensions and fixed points of contractive mappings in ’ (with F. Richman, W. Julian, and R. Mines), J. Math. Analysis and Applications
**165**(2), 438–456, 1992. - ‘Sequential, pointwise, and uniform continuity: a constructive note’, Math. Logic Quarterly
**39**, 55–61, 1993. - ‘Constructive notions of strict convexity’, Math. Logic Quarterly
**39**, 295–300, 1993. - ‘Complements of intersections in constructive mathematics’ (with Hajime Ishihara), Math. Logic Quarterly
**40**, 35–43, 1994. - ‘Sets, complements and boundaries’ (with Fred Richman and Wang Yuchuan), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.)
**7**(4), 425–445, 1996. - ‘Sequentially continuous linear mappings in constructive analysis’ (with Ray Mines), J. Symbolic Logic
**63**(2), 579–583, 1998. - ‘Weak continuity properties in constructive analysis’ (with Luminiţa Dediu), Logic Journal of the IGPL
**7**(3), 277–281, 1999. - ‘Sequential Compactness in Constructive Analysis’ (with Hajime Ishihara and Peter Schuster), Österr. Akad. Wiss. Math.–Natur. Kl. Sitzungsber. II.
**208**, 159–163, 1999 (published in July 2000). - ‘Sequential continuity of functions in recursive analysis’ (with Ayan Mahalanobis), Mathematical Logic Quarterly
**46**(1), 2000, 139-143. - ‘Converses of Bishop’s lemma on located sets’, Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.).
**11**(1), 31–38, 2000. - ‘Increasing, nondecreasing, and virtually continuous functions’ (with Ayan Mahalanobis), J Automata, Languages and Combinatorics
**6**(2), 139–143, 2001. - ‘Dini’s Theorem: a constructive case study’, in:
*Combinatorics, Computability and Logic*(Proceedings of DMTCS’01, Constanţa, Romania, 2–6 July 2001; C.S. Calude, M.J. Dinneen, S. Sburlan (eds.)), 69–80, DMTCS Series**17**, Springer–Verlag, London, 2001. - ‘Compactness and continuity, constructively revisited’ (with Hajime Ishihara and Peter Schuster), in:
*Computer Science Logic*(J. Bradfield, ed; Proceedings of 16th International Workshop CSL 2002, 11th Annual Conference of the EACSL, Edinburgh, Scotland, September 22–25), Lecture Notes in Computer Science**2471**, 89–102, Springer–Verlag, Berlin and Heidelberg, 2002. - ‘Kernels of seminorms in constructive analysis’ (with Nicholas F. Dudley Ward), Theoretical Comp. Sci.
**284**, 259–267, 2002. - ‘Exact, continuous boundary crossings out of convex sets in ’ (with Gabriela Popa), Quart. J. Math.
**54**, 391–398, 2003. - ‘Ishihara’s proof technique in constructive analysis’ (with Dirk van Dalen and Hajime Ishihara), Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) N.S.,
**14**(2), 163–168, 2003. - ‘Constructive complements of unions of two closed sets’, Math. Logic Quarterly
**50**(3), 293–294, 2004. - ‘Computing infima on convex sets, with applications in Hilbert space’ (with Hajime Ishihara and Luminiţa Vîţă), Proc. Amer. Math. Soc.
**132**(9), 2723–2732, 2004. - ‘A new constructive version of Baire’s Theorem’ (with Hajime Ishihara and Luminiţa Vîţă), Hokkaido Math. Journal
**35**(1), 107–118, 2006.

### Miscellaneous constructive papers

- ‘On recursive bounds for the exceptional values in speed–up’ (with Cristian Calude), Theoretical Computer Science
**132**, 387–394, 1994. - ‘Linear independence without choice’ (with Fred Richman and Peter Schuster), Annals of Pure and Applied Logic
**101**(1), 95–102, 1999. - ‘A weak countable choice principle’ (with Fred Richman and Peter Schuster), Proc. Amer. Math. Soc.
**128**(9), 2749–2752, 2000. - ‘First steps in constructive game theory’, Math. Logic Quarterly
**50**(4/5), 501–506, 2004. - ‘Reality and virtual reality in Mathematics’, in:
*Millennium III*(C.S. Calude and K. Svozil, eds), Black Sea University and Romanian Academy, Bucharest, Romania, Autumn 2001. Also in Bull. European Assoc. for Theoretical Computer Science**78**, 221–230, 2002.

### Real and complex analysis

- ‘Geometric intuition and elementary constructive analysis’, Zeit. math. Logik Grundlagen Math.
**25**, 521–523, 1979. - ‘On Montel’s proof of the Great Picard theorem’, Amer. Math. Monthly
**88**(1), 45–47, 1981. - ‘On the isolation of zeroes of an analytic function’, Pacific J. Math.
**96**(1), 13–22, 1981. - ‘Picard’s theorem’ (with A. Calder, W. Julian, R. Mines, and F. Richman), Trans. Amer. Math. Soc.
**269**(2), 513–520, 1982. - ‘A general constructive intermediate value theorem’, Zeit. math. Logik Grundlagen Math.
**35**, 433–435, 1989. - ‘A constructive look at the real number line’, in
*Synthèse: Real Numbers, Generalizations of the Reals and Theories of Continua*(P. Ehrlich, ed.), pp. 29–92, Kluwer Academic Publishers, Amsterdam, 1994. - ‘The constructive implicit function theorem and applications in physics’ (with C. Calude, B. Pavlov, and D. Ştefănescu), Chaos, Solitons & Fractals
**10**(6), 927–934, 1999. - ‘A constructive look at functions of bounded variation’, Bull. London Math. Soc.
**32**(3), 316–324, 2000. - ‘Bounded variation implies regulated: a constructive proof’ (with Ayan Mahalanobis), J. Symbolic Logic.
**66**(4), 1695–1700, 2001. - ‘Constructing local optima on a compact interval’, to appear in Archiv für Math. Logik.

### Set theory

- ‘A note on Morse’s lambda notation in set theory’, Zeit. math. Logik Grundlagen Math.
**24**, 113–114, 1978. - ‘A constructive Morse theory of sets’, in
*Mathematical Logic and its Applications*(D. Skordev, ed.), Plenum Publishing Corp., New York, 61–79, 1987.