Research
Mathematical
logic: Constructive set theory, constructive mathematics and Proof
theory.
Foundations
of mathematics: Constructive foundations and predicativity.
I have recently been supported by a research grant awarded by the John Templeton
Foundation, working on the project: "Infinity in constructive mathematics".
From July 2009 I am working as RA in an EPSRC founded project, PA Michael
Rathjen, title: "Constructive
set theory: Models, independence results and mathematics".
Selected
publications and preprints
- From
sets and types to topology and analysis: towards practicable
foundations for constructive mathematics,
with P. Schuster (eds., co-authored introduction), Oxford Logic Guides
48, Oxford University Press, October 2005, pp. xix + 376.
- Explicit
operational set theory, with A. Cantini, accepted for
publication.
Pdf
- Constructive
notions of sets
(Part II): Sets in Zermelo-Fraenkel set theory, in
preparation.
- Constructive and
Intuitionistic ZF, in Stanford
Encyclopedia
of Philosophy:
http://plato.stanford.edu/entries/set-theory-constructive/ .
- Constructive set
theory with
operations, with A. Cantini,
in Logic Colloquium 2004, A. Andretta,
K. Kearnes,
D. Zambella
(eds.), Association of Symbolic Logic, Lecture Notes in Logic, 29, 2008.
- Constructive
notions of set
(Part I): Sets in Martin- Löf
type theory,
Annali del Dipartimento di Filosofia,
Nuova serie XI, Firenze University Press 2006, pp. 347-387.
- Binary refinement
implies
discrete exponentiation,
with
P. Aczel,
H. Ishiara,
E. Palmgren,
P. Schuster, Studia
Logica,
84 (2006), pp.367-374.
- On constructing
completions,
with H. Ishihara, P.
Schuster, Journal of symbolic Logic 70 (2005), pp.
969-978.
- Inaccessible set
axioms
may
have little consistency strength,
with M. Rathjen,
Annals of Pure and Applied Logic, Vol
115/1-3, pp. 33-70, 2002.
- Tutorial for Minlog,
Mathematisches
Institut
der
LMU Muenchen,
2001, pp. 26
- Realizability
interpretations for
constructive set theories with restricted induction,
PhD thesis, School of Mathematics, University of Leeds. September
2000.
Events
organisation
With Peter
Schuster: workshop From
sets and types to topology and Analisys:
towards practicable foundations for constructive mathematics,
Venice
(Italy),
12-16 May 2003.
With Arnold
Beckmann: special session Proofs
and computation,
Cie
2005: New computational Paradigms,
Amsterdam
(Holland),
8-12 June 2005.
I've
been in the programme
committee of
CiE
2006: Logical approaches to computational barriers,
Swansea (UK),30 June - 5 July 2006, and
CiE
2007: Computation and logic in the real world,
Siena (Italy),
18-23 June 2007.
With Michael Rathjen and Stan Wainer:
Leeds Symposium on Proof Theory and Constructivism
Leeds, 3-16 July 2009
Links
Leeds Logic Group
Computability
in Europe
My
web page, Logic and philosophy
of science group at the Philosophy Department, Florence.
My
web page at the
Mathematisches
Institut
der
LMU München.
My old web
page at the School of
Mathematics of the University of Leeds.
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