Geodesic
The tree property at both $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$
Laura Fontanella1 ; Sy David Friedman1
1 Kurt Gödel Research Center for Mathematical Logic University of Vienna 1090 Wien, Austria
Fundamenta Mathematicae, Tome 229 (2015) no. 1, pp. 83-100 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We force from large cardinals a model of ${\rm ZFC }$ in which $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$ both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model $\aleph _{\omega +2}$ even satisfies the super tree property.
DOI : 10.4064/fm229-1-3
Keywords: force large cardinals model zfc which aleph omega aleph omega have tree property prove strengthen large cardinal assumptions final model aleph omega even satisfies super tree property

Laura Fontanella 1 ; Sy David Friedman 1

1 Kurt Gödel Research Center for Mathematical Logic University of Vienna 1090 Wien, Austria 
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Laura Fontanella; Sy David Friedman. The tree property at both $\aleph _{\omega +1}$ and $\aleph _{\omega +2}$. Fundamenta Mathematicae, Tome 229 (2015) no. 1, pp. 83-100. doi: 10.4064/fm229-1-3

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