{"id":347702,"date":"2017-01-05T19:00:38","date_gmt":"2017-01-06T03:00:38","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=347702"},"modified":"2018-10-16T21:57:58","modified_gmt":"2018-10-17T04:57:58","slug":"148-new-zero-one-law-strong-extension-axioms","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/148-new-zero-one-law-strong-extension-axioms\/","title":{"rendered":"A New Zero-One Law and Strong Extension Axioms"},"content":{"rendered":"

This article is a part of the continuing column on Logic in Computer Science. One of the previous articles in the 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 where every formula uses finitely many variables [Zero-One Laws<\/a>]. 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.<\/p>\n

This publication was also reprinted in 2004 World Scientific book, Current Trends in Theoretical Computer Science<\/i>,\u00a0pages 99-118.<\/p>\n","protected":false},"excerpt":{"rendered":"

This article is a part of the continuing column on Logic in Computer Science. One of the previous articles in the 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 […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Bulletin of the European Association for Theoretical Computer 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