Steve Awodey
Department of Philosophy
Carnegie Mellon University

Research Areas

    Category Theory
    Philosophy of Mathematics
    History of Logic and Analytic Philosophy


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

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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.


·  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)