M. Viale

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math.LO2025

The Boolean Compactness Theorem for $L_{\infty\infty}$

Juan M Santiago SuÃ¡rez, Matteo Viale

We show that, contrary to the commonly held view, there is a natural and optimal compactness theorem for $L_{\infty\infty}$ which generalizes the usual compactness theorem…

math.LO2025

Universality properties of forcing

Francesco Parente, Matteo Viale

The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that an…

math.LO2024

Universally Baire sets in $2^{I^} º$

Daisuke Ikegami, Matteo Viale

We generalize the basic theory of universally Baire sets of $2^{I ¨} $ to a theory of universally Baire subsets of $2^{I^} º$ . We show that the fundamental characterizations of the propert…

The Boolean Compactness Theorem for L∞∞​

Universality properties of forcing

Universally Baire sets in 2I^º

The Boolean Compactness Theorem for $L_{\infty\infty}$

Universally Baire sets in $2^{I^} º$