Year: 2025
Type: preprint
Abstract: We show that, contrary to the commonly held view, there is a natural and optimal compactness theorem for $\mathrm{L}_{\infty\infty}$ which generalizes the usual compactness theorem for first order logic. The key to this result is the switch from Tarski semantics to Boolean valued semantics. On the way to prove it, we also show that the latter is a (the?) natural semantics both for $\mathrm{L}_{\infty\infty}$ and for $\mathrm{L}_{\inftyω}$.
Source: arXiv (Cornell University)
Authors: Suárez, Juan M Santiago, Viale, Matteo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G14893863, G5245466801
OpenAlex ID: W7077045763
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