In this paper, without the axiom of choice, we show that if some downward Lo¨wenheim-Skolem property holds then all grounds are uniformly de- finable. We also prove that the axiom of choice is forceable if and only if the universe is a small extension of some transitive model of ZFC...
In this paper we prove that cats (compact abstract theories,see [Be03]) satisfy a version of Tarski-Vaught test (Theorem 3.1), a version of DLST (downward L¨owenheim-Skolem Tarski) theorem using density character instead of cardinality (Theorem 3.3) and the DAP property (disjoint amalgamatio...
In this paper we prove that cats (compact abstract theories, see [Be03]) satisfy a version of Tarski-Vaught test (Theorem 3.1), a version of DLST (downward L篓owenheim-Skolem Tarski) theorem using density character instead of cardinality (Theorem 3.3) and the DAP property (disjoint ...
We propose a proof of the downward L"owenheim-Skolem that relies on strategies deriving from evaluation games instead of the Skolem normal forms. This proof is simpler, and easily understood by the students, although it requires, when defining the semantics of first-order logic to introduce ...
The 2024 AOS Peter R. Stettenheim Service Award was presented to Jennifer Owen for her exceptional service to ornithology and society, while a posthumous honorary award was given to Reed Bowman for his long-standing dedication to the American Ornithological Society. Jennifer Owen, an associate ...