Bases for vector spaces in different models of set theory

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 infinite-dimensional vector space having only finite-dimensional 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:	https://fse.studenttheses.ub.rug.nl/id/eprint/9287

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