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arXiv · 1205.4275

Square principles in Pmax extensions

Andrés Eduardo Caicedo·Paul Larson·Grigor Sargsyan·Ralf Schindler·John Steel·Martin Zeman
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Abstract

By forcing with $\mathbb{P}_{\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\omega_2$ and $\omega_3$ fail. In particular, we obtain a model of $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 + \lnot\square(\omega_2) + \lnot\square(\omega_3)$.

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Andrés Eduardo Caicedo, Paul Larson, Grigor Sargsyan, Ralf Schindler, John Steel, Martin Zeman. 2012-05-18. Square principles in Pmax extensions. https://doi.org/10.1007/s11856-017-1444-8

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