Abstract
Let \(\alpha \in (0,1)_{{\mathbb {R}}}\) be irrational and \(G_n = G_{n,1/n^\alpha }\) be the random graph with edge probability \(1/n^\alpha \); we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for stronger logics: \({\mathbb {L}}_{\infty , \mathbf{k}}, \mathbf{k}\) a large enough natural number and the inductive logic.
Keywords
This work was partially supported by European Research Council grant 338821. Publication 1061 on Shelah’s list. The author thanks Alice Leonhardt for the beautiful typing.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alon, N., Spencer, J.H.: The Probabilistic Method. Wiley-Interscience Series in Discrete Mathematics and Optimization, 3rd edn. Wiley, Hoboken (2008). With an appendix on the life and work of Paul Erdős
Ebbinghaus, H.-D., Flum, J.: Finite Model Theory. SMM, enlarged edn. Springer, Berlin (2006)
Fagin, R.: Probabilities in finite models. J. Symb. Logic 45, 129–141 (1976)
Glebskii, Y.V., Kogan, D.I., Liagonkii, M.I., Talanov, V.A.: Range and degree of reliability of formulas in restricted predicate calculus. Kibernetica 5, 17–27 (1969). Translation of Cybernetics, vol. 5, pp. 142–154
Shelah, S.: Random graphs: stronger logic but with the 0–1 law. In preparation
Spencer, J.: The Strange Logic of Random Graphs. Algorithms and Combinatorics, vol. 22. Springer, Berlin (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Shelah, S. (2015). On Failure of 0-1 Laws. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-23534-9_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23533-2
Online ISBN: 978-3-319-23534-9
eBook Packages: Computer ScienceComputer Science (R0)