On vector spaces over specific fields without choice

DOI10.1002/MALQ.201200049zbMath1278.03082OpenAlexW2001692375MaRDI QIDQ4928965

Eleftherios Tachtsis, Paul E. Howard

Publication date: 19 June 2013

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/malq.201200049

zbMATH Keywords

generating setsbasesindependent setsvector spacesBoolean prime ideal theoreminfinite systems of linear equationsFraenkel-Mostowski permutation modelschoice principlesnon-zero linear functionals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Vector spaces, linear dependence, rank, lineability (15A03) Axiom of choice and related propositions (03E25)

Related Items (6)

On the set-theoretic strength of the $n$-compactness of generalized Cantor cubes ⋮ On infinite‐dimensional Banach spaces and weak forms of the axiom of choice ⋮ On the solvability of systems of linear equations over the ring $\mathbb{Z}$ of integers ⋮ Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC ⋮ Linear extenders and the Axiom of Choice ⋮ On certain non-constructive properties of infinite-dimensional vector spaces

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