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Vaught Conjecture

OK Having only one sibling of a given rank is bad. Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says "sibling but not any iteration of favorite sibling". Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. How about making the functions one to one? I still don't see the problem here. Posted by Clifton 9:14 AM. Monday, May 23, 2005.

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Vaught Conjecture | vaught.blogspot.com Reviews

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OK Having only one sibling of a given rank is bad. Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says sibling but not any iteration of favorite sibling. Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. How about making the functions one to one? I still don't see the problem here. Posted by Clifton 9:14 AM. Monday, May 23, 2005.

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Vaught Conjecture | vaught.blogspot.com Reviews

https://vaught.blogspot.com

OK Having only one sibling of a given rank is bad. Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says "sibling but not any iteration of favorite sibling". Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. How about making the functions one to one? I still don't see the problem here. Posted by Clifton 9:14 AM. Monday, May 23, 2005.

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Vaught Conjecture: just a thought

http://www.vaught.blogspot.com/2005/05/just-thought.html

Monday, May 23, 2005. What if in addition to having a scott game played only on limit ordinals, we have one that's played only on eldest children? Will this allow us to avoid the L {2 omega, omega} sentence eliminating the Eldest infinity case? By the way, it came up in the last talk that a class is pseudo-elementary L { omega 1, omega} iff it is Sigma 1 1, so ordinals aren't a pseudo-elementary class. But divisible abelian groups have omega 1 many order types (according to Hodge's Model Theory) .

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Vaught Conjecture: May 2005

http://www.vaught.blogspot.com/2005_05_01_archive.html

OK Having only one sibling of a given rank is bad. Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says "sibling but not any iteration of favorite sibling". Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. How about making the functions one to one? I still don't see the problem here. Posted by Clifton 9:14 AM. Monday, May 23, 2005.

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Vaught Conjecture

http://www.vaught.blogspot.com/2005/05/ok.html

Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says "sibling but not any iteration of favorite sibling". Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. The same objection can be raised by replacing the favorite sibling function by a relation that holds between any siblings of rank alpha and alpha 1 respectively. To the Healthc...

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Vaught Conjecture

OK Having only one sibling of a given rank is bad. Tuesday, May 24, 2005. OK Having only one sibling of a given rank is bad. The favorite sibling function will give a successor, and one will have the type that says "sibling but not any iteration of favorite sibling". Then there seems to be no reason (above omega 2) that one couldn't have a model with two siblings of a single rank. How about making the functions one to one? I still don't see the problem here. Posted by Clifton 9:14 AM. Monday, May 23, 2005.

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