Steve Awodey
Professor
Department of Philosophy
Carnegie Mellon University


Research Areas

    Category Theory
    Logic
    Philosophy of Mathematics
    History of Logic and Analytic Philosophy


Textbook

    Category Theory, Oxford Logic Guides, Oxford University Press, 2006

Click here for more information.


Selected Current Preprints
 

·  Homotopy theoretic models of identity types.    

S. Awodey, M. Warren, 2009.
 

·  From sets, to types, to categories, to sets.    

S. Awodey, 2009.
 

·  Lawvere-Tierney sheaves in algebraic set theory.    

S. Awodey, N. Gambino, P. Lumsdaine, M. Warren, 2008.
 

·  A brief introduction to algebraic set theory.    

S. Awodey, 2008.
 

·  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
 

·  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).
 

·  Propositions as [types].    

S. Awodey and A. Bauer, Journal of Logic and Computation 14(4), pp. 447--471 (2004).
 

·  An answer to G. Hellman's question "Does category theory provide a framework for mathematical structuralism?"    

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.


Dissertation
 

·  Logic in Topoi: Functorial Semantics for Higher-Order Logic    

Ph.D. Dissertation, The University of Chicago (1997).
              [Abstract] [Summary]


Editorial Activities
 

·  The Bulletin of Symbolic Logic, reviews 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
 

·  Category Theory  

·  Categorical Logic  

·  Constructive Logic  

·  Logic and Computation


Other Links

Algebraic Set Theory
Pure and Applied Logic Program

Philosophy Department Home

CMU Home

Paintings by Marc Awodey

Categorical Logic Workshop in Japan: Tohoku/Kyoto


Contact Information

Steve Awodey
Department of Philosophy
Carnegie Mellon University
135 Baker Hall
Pittsburgh, PA  15213

Office: BH 152
Phone: (412) 268-8947
Fax: (412) 268-1440
E-Mail: awodey (at) cmu.edu