Some publications and preprints

2016.03 The semantics of the canonical commutation relations (pdf) March 2016 (replacing 2014.08);

2016.01 Analytic Zariski structures and non-elementary categoricity (pdf) January 2016 (extension of 2008.07); arxiv 1601.02961

2015.11 (with L.Shaheen) Model theory and geometry of representations of rings of integers (pdf) January 2016; arxiv 1601.02957

2015.01 (with J.A.Cruz Morales)

  • The geometric semantics of algebraic quantum mechanic Phil. Trans. R. Soc. A 2015 373 20140245; DOI: 10.1098/rsta.2014.0245. Published 29 June 2015

    2014.01 (with J.-D. Caycedo Casallas)

  • Natural theories of models of green points arxiv 1401.3326v1

    2013.08 Model theory of special subvarieties and Schanuel-type conjectures (pdf) Annals of Pure and Applied Logic, Volume 167, Issue 10, October 2016, Pages 1000-–1028;

    2012.10 (with K.Tent) A non-desarguesian projective plane October 2012; arXiv:1510.06176

    2011.08 (with J.Kirby)

  • Exponentially Closed Fields and the Conjecture on Intersections with Tori Annals of Pure and Applied Logic 165. pp. 1680-1706

    2011.12.1 The theory of exponential sums (pdf) December 2011. Replacing "Raising to powers revisited" - 2004.08;.

    2011.12 Perfect infinities and finite approximation(pdf) In: Infinity and Truth. IMS Lecture Notes Series, V.25, 2014

    2010.12 A curve and its abstract Jacobian (pdf) International Mathematical Research Notices, 2012

    2010.01 On model theory, non-commutative geometry and physics(pdf) Draft, January 2010

    2009.10 Structural approximation(pdf) Draft, September 2009

    2009.9 The noncommutative torus and Dirac calculus(pdf) Draft, October 2010

    2008.09 (with T.Kotek and J.Makowsky; extension of 2006.12)

  • On Counting Generalized Colorings, Lect Notes in Computer Sc., V 5213, 2008, pp.339-353

    2008.07 Analytic Zariski structures, predimensions and non-elementary stability(pdf) July 2008

    2008.06 (with V.Solanki) The Quantum Harmonic Oscillator as a Zariski Geometry(pdf) September 2009; Incorporated in ''Quantum Harmonic Oscillator as Zariski Geometry'' (joint with D.Sustretov and V.Solanki), APAL, 165, Issue 6, June 2014, 1149-1168

    2007.04 Non-commutative Zariski geometries and their classical limit(dvi)(pdf) Confluentes Mathematici, v.2,issue 2 , 2010, pp. 265-291

    2007.03 (with M.Bays) Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic. Bull. London Math. Soc. (2011) (Also corrects "Covers of Multiplicative Groups of Algebraically Closed Fields", arXive math.AC/0401301)

  • (pdf)

    2006.12 (with J.Makowsky)Polynomial invariants of graphs and totally categorical theories November 2006

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    2006.11 A class of quantum Zariski geometries(pdf) (dvi) In: Model Theory with applications to algebra and analysis, I and II (Z. Chatzidakis, H.D. Macpherson, A. Pillay, A.J. Wilkie editors), Cambridge University Press, Cambridge. 2008

    2006.11 (with O.Belegradek) The model theory of the field of reals with a subgroup of the unit circle J. London Math. Soc. (2) 78 (2008) 563–579 (and Newton Institute preprint server, February 2006)

    2005.09 Non-commutative geometry and new stable structures (dvi)(pdf) September, 2005.

    2004.10 ( with J.Kirby) The uniform Schanuel conjecture over the real numbers. October 2004. Bulletin of LMS

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    2004.09 1991 example by Hrushovski in the light of non-commutative geometry. A case study. (dvi)(ps) New version. September, 2004.

    2004.02 Covers of Multiplicative Groups of Algebraically Closed Fields, arXive math.AC/0401301

    2004.01 (with N.Peatfield) Analytic Zariski structures and the Hrushovski construction Annals of Pure and Applied Logic, Vol 132/2-3 pp 127-180

    2003.08 A remarkable pseudo-analytic structure (dvi)(ps) August, 2003.

    2003.07 Complex roots of unity on the real plane (pdf) April - July 2003.

    2003.06 Bi-coloured fields on the complex numbers (dvi)(ps) JSL, v.69(4), pp.1171-1186

    2003.04 Pseudo-exponentiation on algebraically closed fields of characteristic zero Annals of Pure and Applied Logic, Vol 132 (2004) 1, pp 67-95

    2003.03 Model theory, geometry and arithmetic of the universal cover of a semi-abelian variety (dvi) (pdf) In Model Theory and Applications, ed. L.Belair and el. ( Proc. of Conf. in Ravello 2000) Quaderni di Matematica, v.11, Series edited by Seconda Universita di Napoli, Caserta, 2002 (with later corrections)

    2002.10 A categoricity theorem for quasi-minimal excellent classes. (dvi) (ps) In: Logic and its Applications eds. Blass and Zhang, Cont.Maths, v.380, 2005, pp.297-306

    2002.04 A theory of a generic function with derivations(dvi) Logic and Algebra (ed. Yi Zhang), pp. 85--100, Contemporary Mathematics, Vol 302, AMS, 2002

    2002.03 Covers of the multiplicative group of an algebraically closed field of characteristic zero. (dvi) (ps) J. London Math. Soc. (2), 74(1):41--58, 2006 (see the joint paper 2007.03 with M.Bays below for corrections and extensions)

    2002.01 Raising to powers in algebraically closed fields(pdf) Journal of Mathematical Logic, v.3, no.2, 2003, 217-238

    2001.04 Analytic and pseudo-analytic structures (pdf) Lecture Notes in Logic, 19. Logic Colloquium 2000, Paris; Rene Cori, Alexander Razborov, Stevo Todorcevic, Carol Wood, editors, 2005; 392–408

    2001.01 On systems of exponential sums with real exponents(pdf) Incorporated into 'Exponential sums equations and the Schanuel conjecture', J. London Math. Soc. (2) 65 (2002)

    2000.03 Intersecting varieties with tori(pdf) Incorporated into 'Exponential sums equations and the Schanuel conjecture', J. London Math. Soc. (2) 65 (2002) With December 2001 corrections.

    1999.10 Fields with pseudo-exponentiation(dvi) e-archive math.LO/0012023

    1997.04 Generalized analytic sets(dvi) Translation from Algebra i Logika, Novosibirsk, v.36, N 4 (1997), 361 - 380

    1993.01 Quasi-Riemann surfaces In: Logic: from Foundations to Applications. European Logic Colloquium 1993. Eds W.Hodges, M.Hyland, Ch.Steinhorn, 1996

    1993.04 Model Theory and Algebraic Geometry In: Seminarberichte Nr 93-1, Proc.10th easter Model Theory, April 12-17,1993, pp.202-222, Humboldt Universitat zu Berlin, 1993

    1992.01 Algebraic geometry via model theory(pdf) In: Cont.Maths. v.131(part 3), 1992, pp.523-537

    1990.01 A note on the model theory of the complex field with roots of unity (dvi) Unpublished paper of 1990

    1988.01 Finite homogeneous geometries (pdf) In: 6th Easter Conference in Model Theory Humboldt University, Berin, 1988, Eds. B.Dahn and H.Wolter