Roumen, F.A. (2010) Bases for vector spaces in different models of set theory. Bachelor's Thesis, Mathematics.

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Abstract
In this thesis, we will consider two models of set theory and look at consequences of these models in linear algebra. The first model satisfies the Axiom of Choice;we will show that this is equivalent to existence of bases for all vector spaces. We will also prove that countability of a vector space is sufficient for proving existence of bases without the Axiom of Choice. The second model will be constructed using the forcing technique. It contains an infinitedimensional vector space having only finitedimensional subspaces, which implies that this vector space has no basis.
Item Type:  Thesis (Bachelor's Thesis) 

Degree programme:  Mathematics 
Thesis type:  Bachelor's Thesis 
Language:  English 
Date Deposited:  15 Feb 2018 07:31 
Last Modified:  15 Feb 2018 07:31 
URI:  http://fse.studenttheses.ub.rug.nl/id/eprint/9287 
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