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The nonexistence of unicorns and many-sorted L\'owenheim-Skolem theorems
- Publication Year :
- 2024
-
Abstract
- Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called strongly polite and can be effectively combined with other theories. Toledo, Zohar, and Barrett conjectured that stably infinite and strongly finitely witnessable theories are smooth and therefore strongly polite. They called counterexamples to this conjecture unicorn theories, as their existence seemed unlikely. We prove that, indeed, unicorns do not exist. We also prove versions of the L\"owenheim-Skolem theorem and the {\L}o\'s-Vaught test for many-sorted logic.<br />Comment: To appear in FM24
- Subjects :
- Mathematics - Logic
Computer Science - Logic in Computer Science
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.18912
- Document Type :
- Working Paper