<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d9393200\x26blogName\x3dRecord+My+Mind:+Banal+Records+of+a+Pe...\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dSILVER\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttp://recordmymind.blogspot.com/search\x26blogLocale\x3den_GB\x26v\x3d2\x26homepageUrl\x3dhttp://recordmymind.blogspot.com/\x26vt\x3d6532355751631192781', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>
Record My Mind: Banal Records of a Pedestrian Life

Suffering and evil overwhelm me and I stew in my own juice. 

Saturday, February 21, 2004

2/21/2004 09:41:00 pm - Starting on Undecidability

I am reading the first section of Enderton's "Chapter 3: Undecidability" and trying to finish Homework Assignment 10. While attempting to answer a question* in the assignment, I searched the web for the definition of "descending chain" (I was hoping to understand the term better) and came upon a file which contained a solution to the question I was trying to solve! From the address of the file, I was able to find a webpage from the University of Ottawa that was using Enderton's "A Mathematical Introduction to Logic" as a textbook for a logic course. The page contained answer files to some problems found in Enderton's book! This was what I have been looking for since I started attempting problems in Enderton's book. It's nice to have model solutions as a reference. I have provided the link to this page in my mathematical logic page.

*The question is:

Consider a language with a two-place predicate symbol <, and let B = (N;<) be the structure consisting of the natural numbers with their usual ordering. Show that there is some A elementarily equivalent to B such that <A has a descending chain. (That is, there must be a0,a1,... in |A| such that < ai+1,ai > Î <A for all i.) Suggestion: Apply the compactness theorem.

To do: Complete Homework Assignment 10.

Random comment: This progress update page is a good thing for me because it helps me to stay focused on acheiving my goal.


Post a Comment

© Boon 2005 - Powered for Blogger by Blogger Templates