Book contents
- Frontmatter
- Contents
- Preface
- Workshop and conference on logic, algebra, and arithmetic: Tehran, October 18–22, 2003
- Foreword
- Mathematical logic in Iran: A perspective
- Real closed fields and IP-sensitivity
- Categoricity and quantifier elimination for intuitionistic theories
- Primes and irreducibles in truncation integer parts of real closed fields
- On explicit definability in arithmetic
- From bounded arithmetic to second order arithmetic via automorphisms
- Local-global principles and approximation theorems
- Beatty sequences and the arithmetical hierarchy
- Specker's theorem, cluster points, and computable quantum functions
- Additive polynomials and their role in the model theory of valued fields
- Dense subfields of henselian fields, and integer parts
- A recursive nonstandard model for open induction with GCD property and cofinal primes
- Model theory of bounded arithmetic with applications to independence results
- Ibn-Sina's anticipation of the formulas of Buridan and Barcan
- Remarks on algebraic D-varieties and the model theory of differential fields
- A simple positive Robinson theory with LSTP ≠ STP
- Categories of theories and interpretations
- References
Model theory of bounded arithmetic with applications to independence results
Published online by Cambridge University Press: 30 March 2017
Book contents
- Frontmatter
- Contents
- Preface
- Workshop and conference on logic, algebra, and arithmetic: Tehran, October 18–22, 2003
- Foreword
- Mathematical logic in Iran: A perspective
- Real closed fields and IP-sensitivity
- Categoricity and quantifier elimination for intuitionistic theories
- Primes and irreducibles in truncation integer parts of real closed fields
- On explicit definability in arithmetic
- From bounded arithmetic to second order arithmetic via automorphisms
- Local-global principles and approximation theorems
- Beatty sequences and the arithmetical hierarchy
- Specker's theorem, cluster points, and computable quantum functions
- Additive polynomials and their role in the model theory of valued fields
- Dense subfields of henselian fields, and integer parts
- A recursive nonstandard model for open induction with GCD property and cofinal primes
- Model theory of bounded arithmetic with applications to independence results
- Ibn-Sina's anticipation of the formulas of Buridan and Barcan
- Remarks on algebraic D-varieties and the model theory of differential fields
- A simple positive Robinson theory with LSTP ≠ STP
- Categories of theories and interpretations
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Logic in Tehran , pp. 239 - 247Publisher: Cambridge University PressPrint publication year: 2006
References
[A] , Interpreting classical theories in constructive ones,The Journal of Symbolic Logic, vol. 65 (2000), no. 4, pp. 1785–1812.Google Scholar
[B1] , Bounded Arithmetic, Bibliopolis, Naples, 1986.
[B2] , On model theory for intuitionistic bounded arithmetic with applications to independence results, Feasible Mathematics( and , editors), Birkhauser Boston, Boston, MA, 1990, pp. 27–47.
[B3] , A note on bootstrapping intuitionistic bounded arithmetic,Proof Theory (Leeds, 1990), Cambridge University Press, Cambridge, 1992, pp. 149–169.
[C] , Feasibly constructive proofs and the propositional calculus, Seventh Annual ACM Symposium on Theory of Computing, ACM, New York, 1975, pp. 83–97.
[CT] and , The strength of replacement in weak arithmetic,Nineteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2004), pp. 256–264.
[CU] and , Functional interpretations of feasibly constructive arithmetic,Annals of Pure and Applied Logic, vol. 63 (1993), no. 2, pp. 103–200.Google Scholar
[J1] , A model-theoretic property of sharply bounded formulae, with some applications,Mathematical Logic Quarterly, vol. 44 (1998), no. 2, pp. 205–215.Google Scholar
[J2] , A remark on independence results for sharply bounded arithmetic,Mathematical Logic Quarterly, vol. 44 (1998), no. 4, pp. 568–570.Google Scholar
[K] , Bounded Arithmetic, Propositional Logic, and Complexity Theory,Cambridge University Press, Cambridge, 1995.
[KPT] , , and , Bounded arithmetic and the polynomial hierarchy,Annals of Pure and Applied Logic, vol. 52 (1991), no. 1-2, pp. 143–153.Google Scholar
[M1] , Comparing constructive arithmetical theories based on NP-PIND and coNP-PIND,Journal of Logic and Computation, vol. 13 (2003), no. 6, pp. 881–888.Google Scholar
[M2] , An independence result for intuitionistic bounded arithmetic, submitted.
[Ta] , Sharply bounded arithmetic and the function a - 1, Logic and Computation (Pittsburgh, PA, 1987), Contemporary Mathematics, vol. 106, Amer. Math. Soc., Providence, RI, 1990, pp. 281–288.
[Th] , The Weak Pigeonhole Principle in Models of Bounded Arithmetic, DPhil Thesis, University of Oxford, 2002.
[Z] , Notes on polynomially bounded arithmetic,The Journal of Symbolic Logic, vol. 61 (1996), no. 3, pp. 942–966.Google Scholar