TY - GEN
T1 - The Nonexistence of Unicorns and Many-Sorted Löwenheim–Skolem Theorems
AU - Przybocki, Benjamin
AU - Toledo, Guilherme
AU - Zohar, Yoni
AU - Barrett, Clark
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025
Y1 - 2025
N2 - 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 Löwenheim–Skolem theorem and the Łoś–Vaught test for many-sorted logic.
AB - 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 Löwenheim–Skolem theorem and the Łoś–Vaught test for many-sorted logic.
UR - http://www.scopus.com/inward/record.url?scp=85204642859&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-71162-6_34
DO - 10.1007/978-3-031-71162-6_34
M3 - منشور من مؤتمر
SN - 9783031711619
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 658
EP - 675
BT - Formal Methods - 26th International Symposium, FM 2024, Proceedings
A2 - Platzer, André
A2 - Rozier, Kristin Yvonne
A2 - Pradella, Matteo
A2 - Rossi, Matteo
PB - Springer Science and Business Media Deutschland GmbH
T2 - 26th International Symposium on Formal Methods, FM 2024
Y2 - 9 September 2024 through 13 September 2024
ER -