A New Zero-One Law and Strong Extension Axioms

One of the previous articles in this column was devoted to the zero-one laws for a number of logics playing prominent role in finite model theory: first-order logic FO, the extension FO+LFP of first-order logic with the least fixed-point operator, and the infinitary logic L ,. Recently Shelah proved a new, powerful, and surprising zero-one law. His proof uses so-called strong extension axioms. Here we formulate Shelah's zero-one law and prove a few facts about these axioms. In the process we give a simple proof for a "large deviation" inequality `a la Chernoff. 1 Shelah's Zero-One Law Quisani: What are you doing, guys? Author: We2 are proving a zero-one law which is due to Shelah. Q: Didn't Shelah prove the law? A: Oh yes, he proved it all right, and even wrote it down [14]. Q: So what is the problem? Can't you read his proof? 1 Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA; partially supported by a grant from Microsoft Research. 2 Th...

• Type: Journal
• Year: 2000
• Where: EATCS
• Authors: Andreas Blass, Yuri Gurevich
• Keywords: EATCS 2000, Logic, Zero-one, Zero-one Law