Steve
Awodey
Professor
Department of
Philosophy
Carnegie Mellon
University
Research Areas
Category Theory
Logic
Philosophy of
Mathematics
Early Analytic Philosophy
Current Projects
Homotopy Type Theory and Univalent Foundations. More information on this research program can be found on the site HomotopyTypeTheory.org. Information on the special year 2012-13 on Univalent Foundations at the Institute for Advanced Study can be found on the UF-wiki.
Algebraic
Set Theory. A website containing some information about AST and links to some papers.
Textbook
Category Theory, Oxford Logic
Guides, Oxford University Press, 2006.
Second edition 2010, now in paperback!
Click here for more information.
Click here for a list of errata.
Slides and Resources
·
Homotopy Type Theory and Univalent Foundations.
Slides from a talk at CMU, March, 2012.
Selected Current Preprints
S. Awodey, 2010.
·
First-order logical duality.
S. Awodey and H. Forssell, 2010.
S. Awodey, P. Hofstra, M. Warren, 2009.
·
From sets, to types, to categories, to sets.
S. Awodey, 2009.
·
Algebraic
models of theories of sets and classes.
S. Awodey, H. Forssell, M. Warren, June 2006.
·
Relating
topos theory and set theory via categories of classes.
S. Awodey, C. Butz, A. Simpson, T. Streicher, June 2003.
Research announcement. Bulletin of Symbolic Logic.
Selected Publications ·
Lawvere-Tierney sheaves in algebraic set theory. S. Awodey, N. Gambino, P. Lumsdaine, M. Warren, Journal of Symbolic Logic, 2009. ·
Homotopy theoretic models of identity types. S. Awodey, M. Warren, Mathematical Proceedings of the Cambridge Philosophical Society, 2009.
·
A brief introduction to algebraic set theory. S. Awodey, The Bulletin of Symbolic Logic, 2008. ·
Topology and modality: The topological
interpretation of first-order modal logic. S. Awodey, K. Kishida, The Review of Symbolic Logic, 2008.
·
Carnap's Dream: Gödel, Wittgenstein, and Logical Syntax. S. Awodey, A.W. Carus, Synthese, 2007. ·
Sheaf toposes for realizability (2004). S. Awodey and A. Bauer, Archive
for Mathemtical Logic, 2008. ·
Algebraic
models of intuitionistic theories of sets and classes. S. Awodey and H. Forssell, Theory and
Applications of Categories 15(5),
CT 2004, pp. 147--163 (2004). ·
Predicative
algebraic set theory.
S. Awodey and M. Warren, Theory and Applications
of Categories 15(1), CT 2004, pp.
1--39 (2004). ·
Ultrasheaves and double negation. S. Awodey and J. Eliasson, Notre Dame Journal of
Formal Logic 45(4), pp. 235--245
(2004). S. Awodey and A. Bauer, Journal of Logic and
Computation 14(4), pp. 447--471
(2004). Philosophia Mathematica (3), vol. 12 (2004), pp. 54--64. ·
Modal operators and the formal dual of Birkhoff's completeness theorem.
S. Awodey and J. Hughes, Mathematical Structures
in Computer Science, vol. 13
(2003), pp. 233-258. ·
Categoricity and completeness: 19th century axiomatics to 21st century
semantics. S. Awodey and E. Reck, History and Philosophy of
Logic , 23 (2002), pp. 1-30, 77-94.
·
Elementary axioms for local maps of toposes. S. Awodey and L. Birkedal, Journal of Pure and
Applied Algebra, 177 (2003), pp.
215-230. ·
Local realizability toposes and a modal logic for
computability.
S. Awodey, L. Birkedal, D.S. Scott, Mathematical
Structures in Computer Science,
vol. 12 (2002), pp. 319-334. ·
Topological completeness for higher-order logic. S. Awodey and C. Butz, Journal of Symbolic Logic 65(3), (2000) pp. 1168--82. ·
Topological representation of the lambda-calculus. Mathematical Structures in Computer Science (2000), vol. 10, pp. 81--96. ·
Sheaf representation for topoi. Journal of Pure and Applied Algebra 145 (2000), pp. 107--121. ·
Carnap, completeness, and categoricity: The Gabelbarkeitssatz of 1928. S. Awodey and A.W. Carus, Erkenntnis 54 (2001), pp. 145-172. ·
Structure in mathematics and logic: a categorical perspective.
Philosophia
Mathematica (3), vol. 4 (1996), pp.
209--237. ·
Axiom of choice and excluded middle in categorical logic. Unpublished MS (1995). Dissertation ·
Logic in Topoi: Functorial Semantics for
Higher-Order Logic
Ph.D.
Dissertation, The University of Chicago (1997).
PhD Students
·
Peter Lumsdaine,
Higher categories from type theory,
CMU, Mathematics, 2010.
·
Kohei Kishida,
Generalized topological semantics for first-order modal logic,
University of Pittsburgh, Philosophy, 2010.
·
Henrik Forssell,
First-order logical duality,
CMU, Philosophy, 2008.
·
Michael Warren,
Homotopy-theoretic aspects of constructive type theory,
CMU, Philosophy, 2008.
·
Matthew Jackson,
A sheaf-theoretic approach to measure theory,
University of Pittsburgh, Mathematics, 2006.
·
Jonas Eliasson,
Ultrasheaves,
University of Uppsala, Mathematics, 2003.
·
Jesse Hughes,
A study of categories of algebras and coalgebras,
CMU, Philosophy, 2001.
[Abstract] [Summary]
Editorial Activities
· The Bulletin of Symbolic Logic , reviews managing editor.
·
The
Collected Works of Rudolf Carnap, editor.
·
Full Circle: Publications of the Archives of
Scientific Philosophy,
managing editor.
· The
Bernays Project, project
member.
Course Materials
Other Links
·
Pure and Applied Logic Program
·
Philosophy Department
·
Oregon Programming Languages Summer School 2012
·
Paintings by Marc Awodey
Contact Information
Steve Awodey
Department of Philosophy
Carnegie Mellon University
Pittsburgh, PA 15213
Office: BH 135F
Phone: (412) 268-8947
Fax: (412) 268-1440
E-Mail: awodey(at)cmu.edu