2024.08 On the logical structure of physics and its continuous model(pdf) August 2024
2023.06 Physics over a finite field and Wick rotation(pdf) June 2023
2023.04 An $L_{\omega_1,\omega}-topological invariant(pdf) February 2024, arxiv
2022.04 Non-elementary categoricity and projective o-minimal classes(pdf) December 2024, Model Theory 3:1 (2024), 101 - 117
2021.04/2 (with C.Daw) Modular curves and their pseudo-analytic cover(pdf) April 2021, revised October 2022
2021.04 (with C.Daw) Canonical models of modular curves and Galois action on CM-points (pdf) April 2021, revised October 2022
2021.03 (with A. Cruz Morales and A.Velaveces) Around Logical Perfection (pdf) Theoria, 2021
2020.12 (with R.Abdolahzadi) A model theory section conjecture (pdf) December, 2020
2020.11 Sections and Towers (pdf) November, 2020
2019.05 (with R.Abdolahzadi) Definablity, interpretations and etale fundamental groups (pdf) May, 2019
2017.12 Structural approximation and quadratic quantum mechanics (pdf) December 2017
2016.03 The semantics of the canonical commutation relations (pdf) March 2016 (replacing 2014.08); http://arxiv.org/abs/1604.07745
2016.01 Analytic Zariski structures and non-elementary categoricity (pdf) In Beyond First Order Model Theory, Ed. J.Iovino, Taylor and Francis, 2017, 299-324; arxiv 1601.02961
2015.11 (with L.Shaheen) On algebras and their spectra. The case of rings of integers. (Replacing Model theory and geometry of representations of rings of integers) April 2018
2015.01 (with J.A.Cruz Morales)
2014.01 (with J.-D. Caycedo Casallas)
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; http://arxiv.org/abs/1501.03301
2012.10 (with K.Tent) A non-desarguesian projective plane October 2012; arXiv:1510.06176
2011.08 (with J.Kirby)
2011.12.1 The theory of exponential sums (pdf) December 2011. Replacing "Raising to powers revisited" - 2004.08;.http://arxiv.org/abs/1501.03297
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. With a correction in Th 1.3, May 2017 (thanks to Yu. Tschinkel)
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)
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)
2006.12 (with
J.Makowsky)Polynomial invariants of graphs and totally categorical theories
November 2006
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
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
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
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 Conf.in 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
1984.01 Some model theory of simple algebraic groups (pdf) Coll.Math. v.48 (1984), 2, pp.173-180