Research interests

Research projects

Logical Methods in Epistemology, Semantics, & Philosophy of Mathematics.

Funded by the British Academy.

Interactions between combinatorics of stationary sets, bounded forcing axioms and inner models of set theory

Funded by EPSRC. Oct.03 - Sep.05

Mathematics into Philosophy: analysing complexity theoretic issues in current philosophical theories of epistemology, semantics and truth

Funded by EPSRC. From October 6'th 2005 to Oct. 2006.

Philosophical Theories of Truth, Transfinite Computation, and Infinite Games

Funded by the Templeton Foundation. From Oct. 2008 to Sep. 2010.

Recent papers or preprints

Abstracts

of some of the below.

• Countable Unions of Simple Sets in the Core Model
Journal of Symbolic Logic, 61, No 1., 1996, pp 293-312.
• Determinacy in the Difference Hierarchy of Co-analytic Sets
Annals of Pure and Applied Logic, 80,No.1,1996, pp 69-108.
• &Sigma^1-3 Absoluteness and the Second Uniform Indiscernible with J.R.Steel,
  in the Israeli Journal of Mathematics, 104,1998, 157-190.
• Determinacy and Delta^1-3 Degrees
to appear in Fundamenta Mathematicae. (Currently being rewritten -draft only)
• On Elementary Embeddings of an Inner Model to the Universe with J. Vickers
in the Journal of Symbolic Logic. 66, No.3, Sep. 2001, 1090-1116. ps pdf dvi
• On Successors of Jonsson Cardinals with J. Vickers
in the Archive for Mathematical Logic, 39, No. 6, 2000, 465-473.
• The Length of Infinite Time Turing Machine Computations
in the Bulletin of the London Mathematical Society, 32, No. 2, March 2000, 129-136.
• Eventually Infinite Time Turing Degrees: infinite time decidable reals
in the Journal of Symbolic Logic, 65, No.3, 2000, pp 1193-1203. ps pdf
• 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.
• 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 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.
• 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 Possible Non-homeomorphic Substructures of the Real Line
in Proceedings of the A.M.S., 130 (2002), no. 9, 2771-2775. ps dvi
• On Revision Operators
in Journal of Symbolic Logic, 68, No.2, June 2003, 689-711. ps pdf dvi
• Bounded Martin's Maximum, weak Erdös cardinals and ψ_AC with David Asperó
in Journal of Symbolic Logic, 67 No. 3, Sep. 2002, 1141-1152. ps pdf
• Possible World Semantics for Predicates with Volker Halbach & Hannes Leitgeb
to appear in Proceedings of the Munich 2001 Conference on Intensionality,
Ed. R. Kahle, in Lecture Notes in Logic, vol. 22, 2005, 20-41. dvi 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. dvi ps pdf
• 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
• Ultimate truth vis à vis stable truth
in Review of Symbolic Logic, 1, No. 1, June 2008, 126-142. dvi ps pdf
• Weak systems of determinacy and arithmetical quasi-inductive definitions
  
Revised and submitted version May 09 pdf or: arXiv: 0905.4412; to appear in the Journal for Symbolic Logic
• On the possibility, or otherwise, of hypercomputation
  in British Journal for Philosophy of Science,vol 55, no. 4, Dec. 2004, 739-746 dvi ps
• On a question of Deolalikar, Hamkins & Schindler (This is subsumed by the Bounding Lemmata... paper below)
  ps pdf
• A note on mutual indiscernibles - a gloss on a theorem of Paul Larson.
  ps pdf
• Comparing inductive and circular definitions: parameters, complexity and games
  
  Kai-Uwe Kühnberger, Benedikt Löwe, Michael Möllerfeld, Philip Welch in:
  ILLC Publication series PP-2004-07, also in Studia Logica, 81, (2005), pp 79-98.. text (pdf), text (ps), Abstract.
• 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 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
• 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
• The Undecidability of Propositional Adaptive Logic with L. Horsten,
  in Preprints in Analytical Philosophy, Centre for Logic, University of Leuven,
  No. 7, 2005, pp. 25. also in Synthese 158, No. 1, Sep. 2007, 41-60. pdf
• Non-deterministic halting times for Hamkins-Kidder Turing machines
in ``Logical Approaches to Computational Barriers'', CiE2006,
Eds. A. Beckmann, U. Berger, B. Löwe, J. Tucker, LNCS 3988, 571-574. dvi pdf
• Bounding Lemmata for non-deterministic halting times of transfinite Turing machines
in Theoretical Computer Science, 394, 2008, 223-228. pdf dvi
• Σ* Fine Structure
a chapter for the ``Handbook of Set Theory'', vol. 3,
Eds. M. Foreman, A. Kanamori & M. Magidor. Springer, Dec. 2009, pp 89. 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
• 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
• 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
• 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
• Global Square and Mutual Stationarity at the Aleph_n
with P. Koepke submitted arXiv:0709.4127v1 pdf
• 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
• 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
• Relativistic Computers and Transfinite Computation
in Unconventional Computation 2009, Eds. C. Calude et al. Lecture Notes in Computer Science 5715, 2009.
• Games for Truth
in Bulletin of Symbolic Logic, vol.15, No.4, Dec. 2009, 410-427. pdf
• Discrete transfinite computational machine 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. pdf

Abstracts of (some of) the above.

Talks

siena.ps siena.pdf
swift.ps
St.Andrews BLC on Field
AQI and Determinacy. Amsterdam 12/11/03 .dvi
Necessity as a Predicate Amsterdam 11/12/03 .dvi
AMS Set Theory Special Session, Phoenix Jan.2004 .ps,
Paris May.2004 .ps, .dvi
Barcelona June.2004 .ps, .dvi
Edinburgh Kurt Gödel Conference, March 26'th 2006 ``Games for supervaluation and dependency''.pdf
Kolkata Meeting 5'th January 2007 "Games and Abstract Inductive Definitions"

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Teaching

Bristol
Undergraduate
My most recent courses have been Third year: Logic (Propositional and Predicate Calculus, the Gödel Completeness
and First Incompleteness Theorems); M32000 Set Theory. Fourth Year M1300 Axiomatic Set Theory, an introduction to
Constructibility theory, and Gödel's universe L, of constructible sets.
(The latter two courses are available to enrolled students on Blackboard)

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Link to Mathematical Logic group at Bonn

Scientiae Mathematicae Japonicae

Links to Kobe:

Kobe University

The Group of Foundations of Mathematics and Computer Science

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