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Что (кто) такое Łoś–Tarski preservation theorem - определение
Łoś–Tarski preservation theorem
The Łoś–Tarski theorem is a theorem in model theory, a branch of mathematics, that states that the set of formulas preserved under taking substructures is exactly the set of universal formulas. The theorem was discovered by Jerzy Łoś and Alfred Tarski.
Tarski–Seidenberg theorem
MATHEMATICAL LOGIC
Tarski-Seidenberg theorem
In mathematics, the Tarski–Seidenberg theorem states that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities. The theorem—also known as the Tarski–Seidenberg projection property—is named after Alfred Tarski and Abraham Seidenberg.
Banach-Tarski paradox
IDEA OF TAKING APART AN OBJECT AND CONSTRUCTING TWO IDENTICAL COPIES OF IT
Banach Tarski Paradoxical Decomposition; Banach-Hausdorff-Tarski Paradox; Banach-Hausdorff-Tarski paradox; Hausdorff–Banach–Tarski paradox; Hausdorff-Banach-Tarski paradox; Banach-Tarski; Banach-Tarski paradox; Banach-Tarksi theorem; The Banach-Tarski Paradox; Tarski-Banach paradox; Tarski-Banach Theorem; Banach-Tarski Theorem; Banach-Tarski theorem; Banach–Tarski theorem; Banach–Tarski Theorem; Banach Tarski paradox; Tarski Banach paradox; Tarski Banach theorem; Banach-Tarski Paradox; Banach-Tarksi paradox; Banach Tarski; Banach Tarski Paradox; Hausdorf-Banach-Tarski Paradox; Banach-Tarski sphere dissection; Pea and the Sun; Pea and the Sun paradox; Banach–Tarski; Banach-Tarsky; Banach-Tarsky paradox
<mathematics> It is possible to cut a solid ball into finitely
many pieces (actually about half a dozen), and then put the
pieces together again to get two solid balls, each the same
size as the original.
This paradox is a consequence of the Axiom of Choice.
(1995-03-29)
