A differential-algebraic criterion for obtaining a small maximal Cohen-Macaulay module, Proceedings of the American Mathematical Society 148 (2020), 4165-4177.

(with R. Miller, I. Kalimullin) Degree Spectra for Transcendence in Fields, in Computing with Foresight and Industry: 15th Conference on Computability in Europe, CiE 2019, eds. F. Manea, B. Martin, D. Paulusma, & G. Primiero, Lecture Notes in Computer Science, 11558 (Berlin: Springer-Verlag, 2019), 205--216.

(with Russell Miller, Bjorn Poonen, Alexandra Shlapentokh) A computable functor from graphs to fields, J. Symb. Log. 83 (2018), no. 1, 326–348.

(with Bruce Olberding, William Heinzer, Matt Toeniskotter and Alan Loper) Ideal theory of infinite directed unions of local quadratic transforms, Journal of Algebra 474, 213-239 (online 2017).

The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron, Annales Mathematicae Silesianae 30, 143–179 (online 2016).

The theory of ordinal length, Beiträge zur Algebra und Geometrie; 57, 67-118 (2016).

(with Charles Li) Poincare Series of Non-divisorial Valuations on Two-dimensional Function Fields, JP Journal of Algebra, Number Theory and Applications 36 (2015).

Hochster's small MCM conjecture for three-dimensional weakly F-split rings, Communications in Algebra 45 (2017), 262-274.

O-minimalism, Journal of Symbolic Logic, 79, 355-409 (2013).
      

Dimension and singularity theory for local rings of finite embedding dimension, Journal of Algebra 386 (2013), 1-60.
      

(with Russell Miller) Computably categorical fields via Fermat’s Last Theorem, Computability 2 (2013), 51-65.
      


Classifying singularities up to analytic extensions of scalars is smooth, Annals of Pure and Applied Logic 162 (2011), 836-852
      


Characteristic $p$ methods in characteristic zero via ultraproducts, in "Commutative Algebra: Noetherian and Non-Noetherian Perspectives", Editors: M. Fontana, S. Kabbaj, B. Olberding and I. Swanson, 387-420, Springer (2010).
      

Constructible invariants, J. Algebra 304 (2006), 1059-1089.
      

M. Aschenbrenner and H. Schoutens, Lefschetz extensions, tight  closure, and big Cohen-Macaulay algebras, Israel Journal of Math. 161 (2007), 221-310
      

Bounds in polynomial rings over Artinian local rings, Monatshefte Math. 150 (2007), 249-261.
      

A local flatness criterion for complete modules,  Comm. Algebra 35 (2007), 289-311.
      

Asymptotical homological conjectures in mixed characteristic, Pacific Journal of Math 230 (2007), 427-468.
      

Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two, Bull. BMS 13 (2006), 719-732.
         

Pure subrings of regular rings are pseudo-rational,  Trans. Amer. Math. Soc. 360 (2008), 609-627.
      

Log-terminal Singularities and Vanishing Theorems via non-standard tight closure, J. of Alg. Geom. 14 (2005) 357-390.
         

On the vanishing of Tor for the absolute integral closure,  J. Algebra 275 (2004), 567-574.
         

Canonical big Cohen-Macaulay algebras and rational singularities, Illinois J. Math. 41 (2004), 131-150.
         

Lefschetz Principle applied to symbolic powers, J. of Algebra and its Appl. 2 (2003), 177-187.
         

Non-standard tight closure for affine $\mathbb C$-algebras,  Manu. Math., 111 (2003), 379-412.
         

Projective dimension and the singular locus, Comm. Algebra 31 (2003), 217-239.
         

Mixed characteristic homological theorems in low degrees,  Comp. Rend. Ac. Sci. 336 (2003), 463-466.
         

Number of generators of a Cohen-Macaulay ideal, J. Algebra 259 (2003), 235-242.
         

Computing the minimal number of equations defining an affine curve ideal-theoretically, J. Pure Applied Alg. 177 (2003), 95-101.
         

A non-standard proof of the Briancon-Skoda Theorem, Proc. Amer. Math. Soc. 131 (2003), 103-112.
         

J. Denef and H. Schoutens, On the decidability of the existential theory of $F_p[[t]]$, Valuation Theory and its Applications, Vol. 2 (Saskatoon, 1999), 43-60, Fields Inst. Commun., 33, AMS, 2003.
         

T.S. Gardener and H. Schoutens, Rigid subanalytic sets, Valuation Theory and its Applications, Vol. 1 (Saskatoon, 1999), 141-150, Fields Inst. Commun., 32, AMS, 2002.
         

Recursive sequences and flatness, Rocky Mountain J. of Math. 31, (2001), pp. 1423-1427.
         

Uniform bounds in Algebraic Geometry and Commutative Algebra, in "Connections between Model Theory and Algebraic and Analytic Geometry" (ed. A. Macintyre), Quaderni di Mathematica 6, (2000), pp. 43-93.
         

T.S. Gardener and H. Schoutens, Flattening and subanalytic sets in rigid analytic geometry, Proc. of Lond. Math. Soc. 83 (2001), 681-707.
         

Artin approximation via the model theory of Cohen-Macaulay rings, Logic Colloquium '98: proceedings of the 1998 ASL Meeting held in Prague, Czech Republic (S. Buss, P. Hajek and P. Pudlak), Lect. Notes in Logic, 13 (2000), pp. 409-425.
         

Bounds in cohomology, Israel J. of Math. 116 (2000), 125-169.
         

Embedded resolution of singularities in rigid analytic geometry, Ann. Fac. Sci. Toulouse VIII (1999), 297-330.
         

Existentially closed models of the theory of Artinian local rings, J. Symb. Logic, 64 (1999), 825-845.
         

Rigid analytic flatificators, Quart. J. Math. Oxford Ser. (2) 50 (1999), 321-353.
         

The closure of rigid semianalytic sets, J. Algebra. 198 (1997), 120-134.
         

Blowing up in rigid analytic geometry, Bull. Soc. Math. Belg. 2 (1994), 401-419.

Rigid subanalytic sets in the plane, J. Algebra 170 (1994), no. 1, 266-276.

Rigid subanalytic sets, Compositio Math. 94 (1994), 269-295.

Uniformization of rigid subanalytic sets, Compositio Math. 94 (1994), 227-245.

Approximation properties for some non-noetherian local rings, Pacific J. Math. 131 (1988), 331-359.