· 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
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
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
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
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.
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
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.
· 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
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.
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.