On failure of 0-1 laws

Saharon Shelah

doi:10.1007/978-3-319-23534-9_18

On failure of 0-1 laws

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

Let α ∈ (0, 1)_ℝ be irrational and G_n = G_n,1/n^α be the random graph with edge probability 1/n^α; 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: (Formula presented.), k a large enough natural number and the inductive logic.

Original language	English
Title of host publication	Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday
Editors	Andreas Blass, Bernd Finkbeiner, Nachum Dershowitz, Wolfram Schulte, Lev D. Beklemishev
Publisher	Springer Verlag
Pages	293-296
Number of pages	4
ISBN (Print)	9783319235332
DOIs	https://doi.org/10.1007/978-3-319-23534-9_18
State	Published - 2015
Event	Symposium on Yurifest, 2015 - Berlin, Germany Duration: 11 Sep 2015 → 12 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9300
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Symposium on Yurifest, 2015
Country/Territory	Germany
City	Berlin
Period	11/09/15 → 12/09/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Keywords

Finite model theory
Inductive logic
Infinitary logic on finite structures
Random graphs
Zero-one laws

Access to Document

10.1007/978-3-319-23534-9_18

Cite this

Shelah, S. (2015). On failure of 0-1 laws. In A. Blass, B. Finkbeiner, N. Dershowitz, W. Schulte, & L. D. Beklemishev (Eds.), Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday (pp. 293-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9300). Springer Verlag. https://doi.org/10.1007/978-3-319-23534-9_18

Shelah, Saharon. / On failure of 0-1 laws. Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday. editor / Andreas Blass ; Bernd Finkbeiner ; Nachum Dershowitz ; Wolfram Schulte ; Lev D. Beklemishev. Springer Verlag, 2015. pp. 293-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Let α ∈ (0, 1)ℝ be irrational and Gn = Gn,1/nα be the random graph with edge probability 1/nα; 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: (Formula presented.), k a large enough natural number and the inductive logic.",

keywords = "Finite model theory, Inductive logic, Infinitary logic on finite structures, Random graphs, Zero-one laws",

author = "Saharon Shelah",

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Shelah, S 2015, On failure of 0-1 laws. in A Blass, B Finkbeiner, N Dershowitz, W Schulte & LD Beklemishev (eds), Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9300, Springer Verlag, pp. 293-296, Symposium on Yurifest, 2015, Berlin, Germany, 11/09/15. https://doi.org/10.1007/978-3-319-23534-9_18

On failure of 0-1 laws. / Shelah, Saharon.
Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday. ed. / Andreas Blass; Bernd Finkbeiner; Nachum Dershowitz; Wolfram Schulte; Lev D. Beklemishev. Springer Verlag, 2015. p. 293-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9300).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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KW - Finite model theory

KW - Inductive logic

KW - Infinitary logic on finite structures

KW - Random graphs

KW - Zero-one laws

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Shelah S. On failure of 0-1 laws. In Blass A, Finkbeiner B, Dershowitz N, Schulte W, Beklemishev LD, editors, Fields of Logic and Computation II - Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday. Springer Verlag. 2015. p. 293-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-23534-9_18

On failure of 0-1 laws

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