My complete list of publications (more than 100 items) is available: PDF, PS, DVI, plain text.
Some of my recent and not-so-recent publications are available for downloading, below. Some information on my books and lecture notes and recent and upcoming talks is available.
Many of my publications and talks deal with foundations of mathematics and reverse mathematics. Some of my recent publications and talks deal with degrees of unsolvability and algorithmic randomness.
My paper Turing degrees of hyperjumps (2020, with Jananthan) is available: PDF. This paper has been submitted for publication.
My paper Pseudojump inversion in special r. b. Pi01 classes (2020, with Jananthan) is available: PDF, DVI. This paper has been submitted for publication.
My paper Foundations of mathematics: an optimistic message (2016) is available: PDF. A version of this paper has been published in a volume of papers in honor of Kurt Schütte.
My paper Turing degrees and Muchnik degrees of recursively bounded DNR functions (2016) is available: PDF, PS, DVI. This paper has been published in a Festschrift in honor of Rod Downey.
My paper Mass problems and density (2015, with Binns and Shore) is available: PDF, PS, DVI. This paper has been published in the Journal of Mathematical Logic.
My paper Reverse mathematics, Young diagrams, and the ascending chain condition (2015, with Hatzikiriakou) is available: PDF, PS, DVI. This paper has been published in the Journal of Symbolic Logic.
My paper Degrees of unsolvability: a tutorial (2015) is available: PDF, PS. This paper has been published in the proceedings volume of Computability in Europe (CiE 2015).
My paper Mass problems and intuitionistic higher-order logic (2014, with Basu) is available: PDF. A version of this paper has been published in Computability.
My paper Cone avoidance and randomness preservation (2013, with Stephan) is available: PDF, PS, DVI. A version of this paper has been published in Annals of Pure and Applied Logic.
My paper Implicit definability in arithmetic (2013) is available: PDF, PS, DVI. This paper has been published in the Notre Dame Journal of Formal Logic.
My paper Propagation of partial randomness (2012, with Higuchi and Hudelson and Yokoyama) is available: PDF, PS, DVI. A version of this paper has been published in Annals of Pure and Applied Logic.
My paper Baire categoricity and Sigma01 induction (2012) is available: PDF, PS, DVI. This paper has been published in the Notre Dame Journal of Formal Logic.
My paper Reverse mathematics and Peano categoricity (2012, with Yokoyama) is available: PDF, PS, DVI. This paper has been published in Annals of Pure and Applied Logic.
My philosophical paper Toward objectivity in mathematics (2009) is available: PDF, PS, DVI. And, my related philosophical paper An objective justification for actual infinity? (2011) is also available: PDF, PS, DVI. Both papers have been published as part of the proceedings of a workshop on Infinity and Truth held at the National University of Singapore.
My paper Symbolic dynamics: entropy = dimension = complexity (2011) is available: PDF, PS, DVI. This paper has been published in Theory of Computing Systems.
My paper Schnorr randomness and the Lebesgue Differentiation Theorem (2011, with Pathak and Rojas) is available: PDF, PS, DVI. This paper has been published in Proceedings of the American Mathematical Society.
My survey paper Mass problems associated with effectively closed sets (2010) is available: PDF, PS. This paper has been published in the Tohoku Mathematical Journal.
My paper Mass problems and measure-theoretic regularity (2009) is available: PDF, PS. This paper has been published in Bulletin of Symbolic Logic.
My paper The Gödel hierarchy and reverse mathematics (2008) is available: PDF, PS, DVI. This paper has been published as a part of the volume Kurt Gödel: Essays for his Centennial.
My paper Mass problems and intuitionism (2007) is available: PDF, PS, DVI. This paper has been published in Notre Dame Journal of Formal Logic.
My paper Medvedev degrees of 2-dimensional subshifts of finite type (2007) is available: PDF, PS, DVI. This paper has been published in Ergodic Theory and Dynamical Systems.
My paper Mass problems and hyperarithmeticity (2006, with Cole) is available: PDF, PS, DVI. This paper has been published in the Journal of Mathematical Logic.
My paper Mass problems and almost everywhere domination (2006) is available: PDF, PS, DVI. This paper has been published in Mathematical Logic Quarterly.
My paper Almost everywhere domination and superhighness (2006) is available: PDF, PS, DVI. See also the flattering referee's report. This paper has been published in Mathematical Logic Quarterly.
My paper Some fundamental issues concerning degrees of unsolvability (2005) is available: PDF, PS. This paper has been published in Computational Prospects of Infinity, a volume in the Lecture Notes Series of the Institute for Mathematical Sciences at the National University of Singapore.
My paper Reverse mathematics and Pi^1_2 comprehension (2005, with Mummert) is available: PDF, PS, DVI. This paper has been published in Bulletin of Symbolic Logic.
My paper An extension of the recursively enumerable Turing degrees (2004) is available: PDF, PS, DVI. This paper is controversial and has an interesting publication history: DVI, PDF, PS, HTML. This paper has been published in Journal of the London Mathematical Society.
My paper Mass problems and randomness (2004) is available: PDF, PS, DVI. This paper has been published in Bulletin of Symbolic Logic.
My paper Almost everywhere domination (2004, with Dobrinen) is available: PDF, PS, DVI. This paper has been published in Journal of Symbolic Logic.
My paper An Incompleteness Theorem for beta_n-Models (2004, with Mummert) is available: PDF, PS, DVI. This paper has been published in Journal of Symbolic Logic.
My paper Embeddings into the Medvedev and Muchnik lattices of Pi^0_1 Classes (2003, with Binns) is available: DVI, PDF, PS. This paper has been published in Archive for Mathematical Logic.
My paper A symmetric beta-model (2000) is available: PDF, PS, DVI.
My paper Some conservation results on Weak König's Lemma (2000, with Tanaka and Yamazaki) is available: DVI, PDF, PS. This paper has been published in Annals of Pure and Applied Logic.
My paper Pi^0_1 sets and models of WKL_0 (2000) is available: PDF, PS, DVI. This paper has been published in Reverse Mathematics 2001.
My paper Logic and mathematics (1999) is available: PDF, PS, DVI. It is a survey of logic and foundations of mathematics for the general reader. It was published as a chapter of The Examined Life, edited by Stanley Rosen.
Information about my book Subsystems of Second Order Arithmetic (Springer-Verlag, 1999) is available.
My paper Separation and Weak König's Lemma (1999, with Humphreys) is available: PDF, PS, DVI. A plain text abstract is also available. This paper has been published in Journal of Symbolic Logic.
My paper Located sets and reverse mathematics (1997, with Giusto) is available: DVI, PDF, PS. A plain text abstract is also available. This paper has been published in Journal of Symbolic Logic.
My paper Vitali's Theorem and WWKL (1996, with Brown and Giusto) is available: PDF, PS, DVI. A plain text abstract is also available. This paper has been published in Archive for Mathematical Logic.
My paper Separable Banach space theory needs strong set existence axioms (1996, with Humphreys) is available: PDF, PS, DVI. A plain text abstract is also available. This paper has been published in Transactions of the American Mathematical Society.
My paper On the strength of König's Duality Theorem for countable bipartite graphs (1994) is available: PDF, PS, DVI. A plain text abstract is also available. This paper was published in Journal of Symbolic Logic.
My old paper The Baire Category Theorem in weak subsystems of second-order arithmetic (1993, with Brown) is available in scanned PDF format. This paper was published in Journal of Symbolic Logic.
My old paper Countable valued fields in weak subsystems of second-order arithmetic (1989, with Hatzikiriakou) is available in PDF format. This paper was published in Annals of Pure and Applied Logic.
My old paper Ordinal numbers and the Hilbert Basis Theorem (1988) is available in scanned PDF format. This paper was published in Journal of Symbolic Logic.
My old paper Partial realizations of Hilbert's Program (1988) is available: PDF, PS, DVI. This paper was published in the Journal of Symbolic Logic.
My old paper Logical analysis of some theorems of combinatorics and topological dynamics (1987, with Blass and Hirst) is available in scanned PDF format. This paper was published as part of Contemporary Mathematics, Volume 65, American Mathematical Society.
My old paper Sigma01 induction and factorization of polynomials (1986, with Smith) is available in scanned PDF format. This paper was published in Annals of Pure and Applied Logic.
My old paper Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche folgen von natürlichen Zahlen (1985, with Schütte) is available in scanned PDF format. This paper was published in Archiv für Mathematische Logik und Grundlagenforschung.
My old paper Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume (1985) is available in scanned PDF format. This paper was published in Archiv für Mathematische Logik und Grundlagenforschung.
My old paper BQO theory and Fraïsse's conjecture (1985) is available in scanned PDF format. This paper was published as a chapter of Recursive Aspects of Descriptive Set Theory, by Richard Mansfield and Galen Weitkamp.
My old paper A dual form of Ramsey's Theorem (1984, with Carlson) is available in scanned PDF format. This paper was published in Advances in Mathematics.
My old paper Set-theoretic aspects of ATR0 (1982) is available in scanned PDF format. My old paper Sigma11 and Pi11 transfinite induction (1982) is available in scanned PDF format. These two papers were published in Logic Colloquium '80.
My old paper On the role of Ramsey quantifiers in first-order arithmetic (1982, with Schmerl) is available in scanned PDF format. This paper was published in the Journal of Symbolic Logic.
My old paper The hierarchy based on the jump operator (1980) is available in scanned PDF format. This paper was published in the Kleene Symposium volume.
My old paper Sets which do not have subsets of every higher degree (1978) is available in scanned PDF format. This paper was published in the Journal of Symbolic Logic.
My old paper First-order theory of the degrees of recursive unsolvability (1977) is available in scanned PDF format. This paper was published in Annals of Mathematics.
My old paper A degree-theoretic definition of the ramified analytic hierarchy (1976, with Jockusch) is available in scanned PDF format. This paper was published in Annals of Mathematical Logic.
My old paper Minimal covers and hyperdegrees (1975) is available in scanned PDF format. This paper was published in Transactions of the American Mathematical Society.
Some more of my papers are also available.
t20@psu.edu / 6 January 2021