Papers or preprints (chronologically since 1996)

·       Abstracts  of some of the below.

 

·       Monotone versus non-monotone projective operators, with J. Aguilera, 

o   to appear,  in Bulletin of the London Mathematical Society, pdf, pp7

·       Free Subsets in internally approachable models, 

o   to appear,  in Archive for Mathematical Logic, pdf pp12

·       When cardinals determine the power set: inner models and Härtig quantifier logic, with J. Väänänen, 

o   Sep. 2023,  in Mathematical Logic Quarterly, 69, No. 4, Sep.2023, 460-471. pdf

·       Asymmetric Cut and Choose Games, with P. Holy, P. Schlicht, and C. Turner, 

o   2023,  in Bulletin of Symbolic Logic 29, No. 4, Dec. 2023, 588-625. pdf  

·       Generalisations of Stationarity, Closed and Unboundedness, and Jensen's , with H. Brickhill  

o   in Annals of Pure and Applied Logic, 174, No. 7, April 2023, pp52. pdf   

·       Decision times of infinite computations, with M. Carl and P. Schlicht,  

o   in Notre Dame Journal of Formal Logic, 63, No. 2, 2022, 197-212. pdf  

·       Characterisations of Variant Transfinite Computational Models:
             Infinite Time Turing, Ordinal Time Turing, and Blum-Shub-Smale machines
 

o   in Computability, 10, 2021, 159-180. pdf 

·       Closed Unbounded Classes and the Härtig quantifier model,

o   in Journal of Symbolic Logic, 87, No. 2, June 2022, 564-584.  

·       Gδσ Games and inductive definitions on the reals with J. P. Aguilera  

o   in Journal of Symbolic Logic, 86, No. 4, Dec. 2021, 1676 - 1690. pdf 

·       Stably Measurable Cardinals 

o   in Journal of Symbolic Logic, 86, No 2, June 2020, 448-470. pdf 

·       Games and Ramsey-like Cardinals, with Dan Nielsen 

o   in Journal of Symbolic Logic, 84, No. 1, 2019, 408-437.pdf 

·       Higher Type Recursion for Transfinite Machine Theory

o   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, 

o   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 

o   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, 

o   in Bulletin of Symbolic Logic, 24, No.3, Sep. 2018, 306-318.pdf 

·       Recognizable sets and Woodin cardinals, with Merlin Carl and Philipp Schlicht, 

o   in Annals of Pure and Applied Logic, 169, No. 4, April 2018, 312-332 pdf 

·       Gödel,

o   in The History of Philosophical and Formal Logic, Eds. M. Antonutti, A. Malpass, Bloomsbury, June 2017, 269-291. pdf 

·       Rethinking Revision, 

o   in Journal of Philosophical Logic, 48, No.1, March 2019, 137-154. pdf 

·       Global Reflection Principles, 

o   in the Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015,

o   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, 

o   in the Israel Journal of Mathematics, 228, No. 1, 2018, 1-19, pdf 

·       Obtaining Woodin's Cardinals 

o   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, 

o   in Notre Dame Journal for Formal Logic 56, 1, p. 213-242. pdf 

·       The complexity of dependence, 

o   in the Journal of Philosophical Logic, 44, No.3, June 2015, 337-340. pdf 

·       Syntax without Arithmetic or Concatenation,  Notes 

o   pp11. pdfs 

·       Conceptualism: sets and classes, 

o   pp13. pdfs 

·       Reflecting on Absolute Infinity, with Leon Horsten, 

o   in Journal of Philosophy, 113, Feb. 2016, 89-111. pdf 

·       Local Club Condensation and L-likeness, with P. Holy, and L.Wu 

o   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

o   Eds. G. Sommaruga & T. Strahm, Birkhäuser/Springer Verlag, Basel, 1st Ed., 2015, 161-185. pdf 

·       Turing's Mathematical Work 

o   in the Proceedings of the 6'th European Congress of Mathematics 

EMS Publishing House, 2014, 763-777. pdf 

·       Some observations on truth hierarchies, 

o   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,

o   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 ,

o   Ed. R.Downey, Lecture Notes in Logic, Association for Symbolic Logic, 2013, pp37. pdf 

·       Some Reflections on Alan Turing's Centenary 

o   in the European Mathematical Society Newsletter , 85,Sep. 2012, 32-38. pdf 

·       Gδσ Games and generalized computation 

o   Sep.2015 pdf 

·       Gδσ; Games 

o   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, 

o   in the Mathematical Intelligencer 35, No. 1, 2013, 16-20 pdf 

·       Revision Revisited, with Leon Horsten, Graham Leigh & Hannes Leitgeb 

o   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" 

o   in Review of Symbolic Logic, 4, No.3, Sept. 2011. pdf 

·       Global Square and Mutual Stationarity at the Aleph_n with P. Koepke, 

o   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,

o   in Annals of Pure and Applied Logic, 162 (2011), 863-902. pdf 

·       Determinacy in strong cardinal models 

o   in Journal of Symbolic Logic, 76, No.2, June 2011, 719-728. pdf 

·       Hypermachines with Sy Friedman

o   in Journal of Symbolic Logic, 76, No.2, June 2011, 620-636. pdf 

·       Ramsey-like Cardinals II with Victoria Gitman

o   in Journal of Symbolic Logic, 76, No.2, June 2011, 541-560. pdf 

·       Weak systems of determinacy and arithmetical quasi-inductive definitions

o   in Journal of Symbolic Logic, 76, No.2, June 2011, 418-436. pdf 

·       3-Pi^1_1 Determinacy

o   Sketch proof of Martin’s theorem that 3-Pi^1-1-Det implies 0^#  pdf

·       Discrete transfinite computation models

o   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 

o   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 

o   in Theoretical Computer Science, vol. 410, Jan. 2009, 426-442 doi: 10.1016/j.tcs.2008.09.050, pdf 

·       Turing Unbound: Transfinite Computation 

o   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 

o   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, 

o   Eds. M. Foreman, A. Kanamori & M. Magidor. Springer, Dec. 2009, 657-745. ps 

·       Games for Truth 

o   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 

o   in Mind, vol. 118, No.469, pp71-100; Jan. 2009 pdf 

·       Turing Unbound: on the extent of computation in Malament-Hogarth spacetimes 

o   in British Journal for the Philosophy of Science, vol 59. No.4, Dec. 2008, 659-674. pdf ps 

·       Field on Revenge with Agustin Rayo, 

o   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 

o   in Review of Symbolic Logic, 1, No. 1, June 2008, 126-142. dvi ps pdf 

·       The Undecidability of Propositional Adaptive Logic with L. Horsten,

o   in Synthese 158, No. 1, Sep. 2007, 41-60. pdf 

·       Bounding Lemmata for non-deterministic halting times of transfinite Turing machines 

o   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

o   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

o   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

o   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

o   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. 

o   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,

o   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

o   in Archive for Mathematical Logic, 43 (2004), no. 4, 443-458. ps dvi 

·       On a question of Deolalikar, Hamkins & Schindler

o   (This preprint is subsumed by the Bounding Lemmata... paper above) ps pdf 

·       Post's and other problems in higher type supertasks 

o   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

o   in Journal of Philosophical Logic, 32 No.3, April 2003, 179-223. dvipspdf 

·       On Revision Operators 

o   in Journal of Symbolic Logic, 68, No.2, June 2003, 689-711. ps pdf dvi 

·       Pf does not equal NPf for almost all f  with Joel Hamkins 

o   in Mathematical Logic Quarterly, 49, No.5, 2003, 536-540. dvi ps pdf 

·       Bounded Martin's Maximum, weak ErdQs cardinals and ψAC with David Asperó

o   in Journal of Symbolic Logic, 67 No. 3, Sep. 2002, 1141-1152. ps pdf 

·       On Possible Non-homeomorphic Substructures of the Real Line 

o   in Proceedings of the A.M.S., 130 (2002), no. 9, 2771-2775. ps dvi 

·       Some remarks on the Maximality of Inner Models 

o   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

o   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

o   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,

o   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

o   in Journal of Symbolic Logic, 65, No.3, 2000, pp 1193-1203. ps pdf 

·       The Length of Infinite Time Turing Machine Computations

o   in Bulletin of the London Mathematical Society, 32, No. 2, March 2000, 129-136. 

·       On Successors of Jonsson Cardinals with J. Vickers

o   in Archive for Mathematical Logic, 39, No. 6, 2000, 465-473. 

·       Friedman's Trick: Minimality Arguments in the Infinite Time Turing Degrees,

o   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

o   to appear in Fundamenta Mathematicae. (Currently being rewritten -draft only) 

·       Σ13 Absoluteness and the Second Uniform Indiscernible with J.R.Steel,

o   in Israeli Journal of Mathematics, 104,1998, 157-190. 

·       Determinacy in the Difference Hierarchy of Co-analytic Sets

o   in Annals of Pure and Applied Logic, 80,No.1,1996, pp 69-108. 

·       Countable Unions of Simple Sets in the Core Model

o   in Journal of Symbolic Logic, 61, No 1, 1996, pp 293-312. 

 

 

 

Lectures on Higher Type ITTM Recursion and Determinacy

·       Notes June 2020