Book contents
- Frontmatter
- Contents
- Introduction
- Historical remarks on Suslin's problem
- The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture
- ω-models of finite set theory
- Tennenbaum's theorem for models of arithmetic
- Hierarchies of subsystems of weak arithmetic
- Diophantine correct open induction
- Tennenbaum's theorem and recursive reducts
- History of constructivism in the 20th century
- A very short history of ultrafinitism
- Sue Toledo's notes of her conversations with Gödel in 1972–5
- Stanley Tennenbaum's Socrates
- Tennenbaum's proof of the irrationality of √2
- References
Diophantine correct open induction
Published online by Cambridge University Press: 07 October 2011
Book contents
- Frontmatter
- Contents
- Introduction
- Historical remarks on Suslin's problem
- The continuum hypothesis, the generic-multiverse of sets, and the Ω conjecture
- ω-models of finite set theory
- Tennenbaum's theorem for models of arithmetic
- Hierarchies of subsystems of weak arithmetic
- Diophantine correct open induction
- Tennenbaum's theorem and recursive reducts
- History of constructivism in the 20th century
- A very short history of ultrafinitism
- Sue Toledo's notes of her conversations with Gödel in 1972–5
- Stanley Tennenbaum's Socrates
- Tennenbaum's proof of the irrationality of √2
- 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
- Set Theory, Arithmetic, and Foundations of MathematicsTheorems, Philosophies, pp. 93 - 111Publisher: Cambridge University PressPrint publication year: 2011
References
[1] and , A recursive nonstandard model of normal open induction, The Journal of Symbolic Logic, vol. 61 (1996), no. 4, pp. 1228–1241.Google Scholar
[2] and , Distribution of values of bounded generalized polynomials, Acta Mathematica, vol. 198 (2007), no. 2, pp. 155–230.Google Scholar
[4] , Partially Ordered Rings and Semi-Algebraic Geometry, Cambridge University Press, Cambridge, 1979.Google Scholar
[7] , A non-standard model for a free variable fragment of number theory, Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 12 (1964), pp. 79–86.Google Scholar
[8] , Tame Topology and O-Minimal Structures, Cambridge University Press, Cambridge, 1998.Google Scholar
[9] , Diophantische Ungleichungen, Acta Mathematica, vol. 59 (1932), no. 1, pp. 209–328.Google Scholar
[10] , Some results and problems on weak systems of arithmetic, Logic Colloquium '77 ( et al., editors), North-Holland, Amsterdam, 1978, pp. 285–296.Google Scholar