Papers or preprints (chronologically since 1996)

• Abstracts  of some of the below.

• When cardinals determine the power set: inner models and Härtig quantifier logic, with J. Väänänen, 
• Sep. 2023,  in Mathematical Logic Quarterly, https://doi.org/10.1002/malq.202200030
• Asymmetric Cut and Choose Games, with P. Holy, P. Schlicht, and C. Turner, 
• 2023,  in Bulletin of Symbolic Logic pdf DOI: 10.1017/bsl.2023.31 
• Generalisations of Stationarity, Closed and Unboundedness, and Jensen's ☐, with H. Brickhill,  
•             in Annals of Pure and Applied Logic, 174, No. 7, April 2023, pp52. pdf  https://doi.org/10.1016/j.apal.2023.103272 
• Decision times of infinite computations, with M. Carl and P. Schlicht, 
•             in Notre Dame Journal of Formal Logic, 63, No. 2, 2022, 197-212.  
• Characterisations of Variant Transfinite Computational Models:
  Infinite Time Turing, Ordinal Time Turing, and Blum-Shub-Smale machines, 
•           in Computability, 10, 2021, 159-180.  
• G_δσ Games and inductive definitions on the reals  with J. P. Aguilera
•             in Journal of Symbolic Logic, 86, No. 4, Dec. 2021, 1676 - 1690. pdf 

• Stably Measurable Cardinals 
• in Journal of Symbolic Logic, 86, No 2, June 2020, 448-470. pdf 
• Closed Unbounded Classes and the Härtig quantifier model,
• in Journal of Symbolic Logic, 82, No. 2, June 2022, 564-584.  
• Games and Ramsey-like Cardinals, with Dan Nielsen 
• in Journal of Symbolic Logic, 84, No. 1, 2019, 408-437.pdf 
• Higher Type Recursion for Transfinite Machine Theory
• in Proceedings of Computation in Europe, CiE2019, Eds. F. Manea, B. Martin, D. Paulusma and G. Primiero,
• Springer Lecture Notes in Computer Science, 11558, 72-83 pdf 
• Proving Theorems from Reflection, 
• in Reflections on the Foundations of Mathematics - Univalent Foundations, Set Theory and General Thoughts,
• Eds. S. Centrone, D. Kant, and D. Sarikaya, Synthese Library in Epistemology, Logic, 
• Methodology and Philosophy of Science, 11558, 72-83 pdf 
• Taming Koepke's Zoo with M. Carl and S. Ouazzani 
• in Proceedings of Computation in Europe, CiE2018,
• Eds.F. Manea, R. Miller and D. Nowotka, Springer Lecture Notes in Computer Science, 10936, 126-135 pdf 
• The Ramified Analytical Hierarchy using Extended Logics, 
• in Bulletin of Symbolic Logic, 24, No.3, Sep. 2018, 306-318.pdf 
• Recognizable sets and Woodin cardinals, with Merlin Carl and Philipp Schlicht, 
• in Annals of Pure and Applied Logic, 169, No. 4, April 2018, 312-332 pdf 
• Gödel,
• in The History of Philosophical and Formal Logic, Eds. M. Antonutti, A. Malpass, Bloomsbury, June 2017, 269-291. pdf 
• Rethinking Revision, 
• in Journal of Philosophical Logic, 48, No.1, March 2019, 137-154. pdf 
• Global Reflection Principles, 
• in the Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015,
• Eds. H. Leitgeb, I. Niiniluoto, P. Seppälä and E. Sober. College Publications, June 2017, pp18. pdf 
• Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities, with Dominik Adolf and Sean Cox, 
• in the Israel Journal of Mathematics, 228, No. 1, 2018, 1-19, pdf 
• Obtaining Woodin's Cardinals 
• in ``Logic in Harvard: Conference celebrating the birthday of Hugh Woodin''
• Eds. A. Caicedo, J. Cummings, P.Koellner & P. Larson, AMS Series, Contemporary Mathematics, vol. 690, 161-176, May 2017. pdf 
• Large Cardinals, Inner Models and Determinacy: an introductory overview, 
• in Notre Dame Journal for Formal Logic 56, 1, p. 213-242. pdf 
• The complexity of dependence, 
• in the Journal of Philosophical Logic, 44, No.3, June 2015, 337-340. pdf 
• Syntax without Arithmetic or Concatenation,  Notes 
• pp11. pdfs 
• Conceptualism: sets and classes, 
• pp13. pdfs 
• Reflecting on Absolute Infinity, with Leon Horsten, 
• in Journal of Philosophy, 113, Feb. 2016, 89-111. pdf 
• Local Club Condensation and L-likeness, with P. Holy, and L.Wu 
• in Journal of Symbolic Logic, 80, no. 4, 2015, 1361-1378. pdf 
• Discrete transfinite computation in Turing's Revolution: the impact of his ideas about computability
• Eds. G. Sommaruga & T. Strahm, Birkhäuser/Springer Verlag, Basel, 1st Ed., 2015, 161-185. pdf 
• Turing's Mathematical Work 
• in the Proceedings of the 6'th European Congress of Mathematics 
• EMS Publishing House, 2014, 763-777. pdf 
• Some observations on truth hierarchies, 
• in the Review of Symbolic Logic, 7 No. 1, March 2014 1-30. pdf 
• Global Reflection principles, currently in the Isaac Newton Institute pre-print series, No. NI12051-SAS,
• to appear as part of the Harvard ``Exploring the Frontiers of Incompleteness'' Series volume, 2014, 
• Ed. P. Koellner, pp28. pdf 
• Transfinite Machine Models a chapter in Turing's Legacy ,
• Ed. R.Downey, Lecture Notes in Logic, Association for Symbolic Logic, 2013, pp37. pdf 
• Some Reflections on Alan Turing's Centenary 
• in the European Mathematical Society Newsletter , 85,Sep. 2012, 32-38. pdf 
• G_δσ Games and generalized computation 
• Sep.2015 pdf 
• G_δσ; Games 
• in the Isaac Newton Institute Pre-print series No. NI12050-SAS, July 2012, pdf 
• The Aftermath - a mise en scène in three parts, with L. Horsten, 
• in the Mathematical Intelligencer 35, No. 1, 2013, 16-20 pdf 
• Revision Revisited, with Leon Horsten, Graham Leigh & Hannes Leitgeb 
• in Review of Symbolic Logic, 5, No.4, Dec. 2012, pp642-664. pdf 
• Truth, Logical Validity, and Determinateness: a commentary on Field's "Saving Truth from Paradox" 
• in Review of Symbolic Logic, 4, No.3, Sept. 2011. pdf 
• Global Square and Mutual Stationarity at the Aleph_n with P. Koepke, 
• in Annals of Pure and Applied Logic, 162 (2011), 787-806. pdf 
• Greatly Erdős Cardinals with some generalisations to the Chang and Ramsey properties with I.Sharpe,
• in Annals of Pure and Applied Logic, 162 (2011), 863-902. pdf 
• Determinacy in strong cardinal models 
• in Journal of Symbolic Logic, 76, No.2, June 2011, 719-728. pdf 
• Hypermachines with Sy Friedman
• in Journal of Symbolic Logic, 76, No.2, June 2011, 620-636. pdf 
• Ramsey-like Cardinals II with Victoria Gitman
• in Journal of Symbolic Logic, 76, No.2, June 2011, 541-560. pdf 
• Weak systems of determinacy and arithmetical quasi-inductive definitions
  
• in Journal of Symbolic Logic, 76, No.2, June 2011, 418-436. pdf 
• Discrete transfinite computation models
• a chapter in Computability in Context Computation and Logic in the real world
• Eds. S.B. Cooper & A. Sorbi; Imperial College Press/ World Scientific, 375-414. pdf 
• Relativistic Computers and Transfinite Computation 
• in Unconventional Computation 2009, Eds. C. Calude et al. Lecture Notes in Computer Science 5715, 2009. 
• Characteristics of discrete transfinite Turing machine models:
  halting times, stabilization times, and Normal Form Theorems 
• in Theoretical Computer Science, vol. 410, Jan. 2009, 426-442 doi: 10.1016/j.tcs.2008.09.050, pdf 
• Turing Unbound: Transfinite Computation 
• in Computation and Logic in the Real World Proceedings of CiE-2007 Siena, 
• Eds. S.B. Cooper, B. Löwe, A. Sorbi. Lecture Notes in Computer Science 4497, 2007, 768-780. ps dvi 
• On the consistency of the Inner Model Hypothesis with Sy-David Friedman, W.Hugh Woodin 
• in Journal of Symbolic Logic, 73, No.2, 391-400. pdf dvi ps 
• Σ* Fine Structure  a chapter for the ``Handbook of Set Theory", vol. 1, 
• Eds. M. Foreman, A. Kanamori & M. Magidor. Springer, Dec. 2009, 657-745. ps 
• Games for Truth 
• in Bulletin of Symbolic Logic, vol.15, No.4, Dec. 2009, 410-427. pdf 
• Necessities and Necessary Truths: A Prolegomenon to
  the Use of Modal Logic in the Analysis of Intensional Notions with Volker Halbach 
• in Mind, vol. 118, No.469, pp71-100; Jan. 2009 pdf 
• Turing Unbound: on the extent of computation in Malament-Hogarth spacetimes 
• in British Journal for the Philosophy of Science, vol 59. No.4, Dec. 2008, 659-674. pdf ps 
• Field on Revenge with Agustin Rayo, 
• in The Revenge of the Liar, Ed. J.C. Beall, O.U.P., Feb. 2008, 234-249. pdf dvi ps 
• Ultimate truth vis à vis stable truth 
• in Review of Symbolic Logic, 1, No. 1, June 2008, 126-142. dvi ps pdf 
• The Undecidability of Propositional Adaptive Logic with L. Horsten,
• in Synthese 158, No. 1, Sep. 2007, 41-60. pdf 
• Bounding Lemmata for non-deterministic halting times of transfinite Turing machines 
• in Theoretical Computer Science, 394, 2008, 223-228. pdf dvi 
• Non-deterministic halting times for Hamkins-Kidder Turing machines 
• Some open problems in mutual stationarity involving inner model theory: a commentary
• Proceedings of the Banff Conference on Singular Cardinal Combinatorics.
• in Notre Dame J. of Formal Logic, 46, No.3, 2005, pp.375-379. ps pdf 
• On the transfinite action of 1 tape Turing machines
• in New Computational Paradigms CiE 2005 Proceedings,
• Eds S.B. Cooper, B. Löwe, L. Torenvliet; LNCS vol.3526, 532-539. ps pdf 
• On the strength of mutual stationarity with Peter Koepke
• in ``Set Theory. Centre de recerca Matematica, Barcelona, 2003-2004'', Eds. J. Bagaria, S. Todorcevic,
• Birkhäuser Verlag, Trends in mathematics series Basel, 2006, pp 309-320 ps pdf 
• On the possibility, or otherwise, of hypercomputation
• in British Journal for Philosophy of Science,vol 55, no. 4, Dec. 2004, 739-746 dvi ps 
• A note on mutual indiscernibles - a gloss on a theorem of Paul Larson. 
• ps pdf 
• Possible World Semantics for Predicates with Volker Halbach & Hannes Leitgeb
• Comparing inductive and circular definitions: parameters, complexity and games with Kai-Uwe Kühnberger,
• Benedikt Löwe, Michael Möllerfeld, Philip Welch in Studia Logica, 81, (2005), pp 79-98. text (pdf), text (ps), Abstract. 
• On Unfoldable cardinals, omega-closed cardinals, and the beginning of the Inner Model Hierarchy
• in Archive for Mathematical Logic, 43 (2004), no. 4, 443-458. ps dvi 
• On a question of Deolalikar, Hamkins & Schindler
• (This preprint is subsumed by the Bounding Lemmata... paper above) ps pdf 
• Post's and other problems in higher type supertasks 
• in Classical and New Paradigms of Computation and their Complexity hierarchies, 
• Papers of the Conference Foundations of the Formal Sciences III Eds. Löwe, Piwinger, Räsch, 
• in ``Trends in Logic'' Series, vol. 23, Kluwer, Oct. 2004, 223-237. dvi ps pdf 
• Possible World Semantics for Modalities conceived as predicates with Volker Halbach & Hannes Leitgeb
• in Journal of Philosophical Logic, 32 No.3, April 2003, 179-223. dvipspdf 
• On Revision Operators 
• in Journal of Symbolic Logic, 68, No.2, June 2003, 689-711. ps pdf dvi 
• P^f does not equal NP^f for almost all f  with Joel Hamkins 
• in Mathematical Logic Quarterly, 49, No.5, 2003, 536-540. dvi ps pdf 
• Bounded Martin's Maximum, weak ErdQs cardinals and ψ_AC with David Asperó
• in Journal of Symbolic Logic, 67 No. 3, Sep. 2002, 1141-1152. ps pdf 
• On Possible Non-homeomorphic Substructures of the Real Line 
• in Proceedings of the A.M.S., 130 (2002), no. 9, 2771-2775. ps dvi 
• Some remarks on the Maximality of Inner Models 
• in Proceedings Logic Colloquium '98, Ed. S. Buss, P. Hajek & P. Pudlak, 
• Lecture Notes in Logic, 13, pp 516-540. 
• On Elementary Embeddings of an Inner Model to the Universe with J. Vickers
• in Journal of Symbolic Logic , 66, No.3, Sep. 2001, 1090-1116. ps pdf dvi 
• On Gupta-Belnap Revision Theories of truth, Kripkean Fixed points, and the Next Stable Set
• a Communication in Bulletin of Symbolic Logic, vol 7,No.3, 2001, pp 345-360. ps pdf dvi 
• Set-Theoretic Absoluteness and the Revision Theory of Truth, with Benedikt Löwe,
• in Studia Logica, vol 68, No.1, June 2001, (special issue on "Theories of Truth") 21-41. ps 
• Eventually Infinite Time Turing Degrees: infinite time decidable reals
• in Journal of Symbolic Logic, 65, No.3, 2000, pp 1193-1203. ps pdf 
• The Length of Infinite Time Turing Machine Computations
• in Bulletin of the London Mathematical Society, 32, No. 2, March 2000, 129-136. 
• On Successors of Jonsson Cardinals with J. Vickers
• in Archive for Mathematical Logic, 39, No. 6, 2000, 465-473. 
• Friedman's Trick: Minimality Arguments in the Infinite Time Turing Degrees,
• in "Sets and Proofs" - Proc. Leeds Logic Colloquium, Ed. S.B.Cooper & J.K.Truss, 
• Lond. Math. Soc. Lecture Notes in Mathematics Series, 259, April 1999, C.U.P., pp 425-436. 
• Determinacy and Δ¹₃Degrees
• to appear in Fundamenta Mathematicae. (Currently being rewritten -draft only) 
• Σ¹₃ Absoluteness and the Second Uniform Indiscernible with J.R.Steel,
• in Israeli Journal of Mathematics, 104,1998, 157-190. 
• Determinacy in the Difference Hierarchy of Co-analytic Sets
• in Annals of Pure and Applied Logic, 80,No.1,1996, pp 69-108. 
• Countable Unions of Simple Sets in the Core Model
• in Journal of Symbolic Logic, 61, No 1, 1996, pp 293-312. 

Lectures on Higher Type ITTM Recursion and Determinacy

• Notes June 2020