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View:  Topic list, Topic summary Topics 1 - 10 of 20792  Older »
Description: Logic -- math, philosophy & computational aspects.
 

Dense Linear Ordering problems. 
  I have two clusters of questions. Conjecture 1: ========== Any countable dense linear ordering with no end-points is order-isomorphic to any other. This is easily proved with AC, is that right? In fact, it only needs DC, is that right? But CC is not sufficient, is that right? (I'd guess this is hard.)... more »
By Bill Taylor  - 12:11am - 3 new of 3 messages    

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By Erma FIERRO  - Nov 23 - 1 new of 1 message    

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By NUMBER 1  - Nov 23 - 1 new of 1 message    

Another AC anomaly? 
  Has anyone seen this before? [link] I'm not sure yet what to conclude from it; that AC is horribly wrong, or that WM is horribly right, or something else altogether. In short the story goes like this: A game is played, in which infinitely many coins are tossed, and there's... more »
By Herman Jurjus  - Nov 23 - 25 new of 25 messages    

*** Reminder:FACS/LMS Evening Seminar by Prof Mike Gordon: Forward with Hoare, 1 December 2009, London Mathematical Society, Demorgan House 
  (Apologies if you receive multiple copies of this announcement) BCS-FACS Evening Seminar Series Joint event with the London Mathematical Society Forward with Hoare Professor Mike Gordon, FRS (Cambridge University)... more »
By Paul.Boca@googlemail.com  - Nov 22 - 1 new of 1 message    

A new definition of Cardinality. 
  Hi all, As far as I know, all the definitions of cardinality are limited in a way or another, lets take them one after the other: 1) Von Neumann's Cardinals: A cardinal is the least of all equinumerous ordinals. 2) Frege-Russell Cardinals: A cardinal is an equivalence class of sets under equivalence relation... more »
By zuhair  - Nov 22 - 17 new of 17 messages    

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By studentservice  - Nov 22 - 1 new of 1 message    

Q about Suppes Axiomatic Set Theory 
  This question refers to Definition 3, Section 5.1[1]. The definition reads: A is complete if and only if every member of A is a subset of A. He does not express it in his formal language, explaining why For every x if x \in A then x \subseteq A won't do. So how would one express the definition of 'complete'... more »
By Frederick Williams  - Nov 22 - 4 new of 4 messages    

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