Geodesic
The Boolean prime ideal theorem does not imply the extension of almost disjoint families to MAD families
Eleftherios Tachtsis1
1 Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi 83200, Samos, Greece <a href="https://orcid.org/0000-0001-9114-3661">ORCID: 0000-0001-9114-3661</a>
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 105-115

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We establish that the statement “For every infinite set $X$, every almost disjoint family in $X$ can be extended to a maximal almost disjoint (MAD) family in $X$” is not provable in $\mathsf {ZF}$ + Boolean prime ideal theorem + Axiom of Countable Choice. This settles an open problem from Tachtsis [On the existence of almost disjoint and MAD families without $\mathsf {AC}$, Bull. Polish Acad. Sci. Math. 67 (2019), 101–124].
DOI : 10.4064/ba201014-22-1
Keywords: establish statement every infinite set every almost disjoint family extended maximal almost disjoint mad family provable mathsf boolean prime ideal theorem axiom countable choice settles problem tachtsis existence almost disjoint mad families without mathsf bull polish acad sci math

Eleftherios Tachtsis 1

1 Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi 83200, Samos, Greece <a href="https://orcid.org/0000-0001-9114-3661">ORCID: 0000-0001-9114-3661</a> 
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Eleftherios Tachtsis. The Boolean prime ideal theorem does not imply the extension of almost disjoint families to MAD families. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 105-115. doi: 10.4064/ba201014-22-1

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