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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.

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