List of topics named after Alfred Tarski
Encyclopedia
In the history of mathematics
, Alfred Tarski
(1901–1983) is one of the most important logic
ians. His name is now associated with a number of theorem
s and concepts in that field.
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
, Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
(1901–1983) is one of the most important logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
ians. His name is now associated with a number of theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s and concepts in that field.
Theorems
- Knaster–Tarski theoremKnaster–Tarski theoremIn the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:...
(sometimes referred to as Tarski's fixed point theorem) - Tarski's undefinability theorem
- Tarski–Seidenberg theoremTarski–Seidenberg theoremIn mathematics, the Tarski–Seidenberg theorem states that a set in -dimensional space defined by polynomial identities and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities...
- Some fixed point theorems, usually variants of the Kleene fixed-point theorem, are referred to the Tarski–Kantorovitch fixed–point principle or the Tarski–Kantorovitch theorem although the use of this terminology is limited.
Other
- Banach–Tarski paradoxBanach–Tarski paradoxThe Banach–Tarski paradox is a theorem in set theoretic geometry which states the following: Given a solid ball in 3-dimensional space, there exists a decomposition of the ball into a finite number of non-overlapping pieces , which can then be put back together in a different way to yield two...
- Lindenbaum–Tarski algebraLindenbaum–Tarski algebraIn mathematical logic, the Lindenbaum–Tarski algebra of a logical theory T consists of the equivalence classes of sentences of the theory...
- Jónsson–Tarski duality
- Gödel–McKinsey–Tarski translation
- The semantic theory of truthSemantic theory of truthA semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.-Origin:The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work published by Polish...
is sometimes referred to as Tarski's definition of truth or Tarski's truth definitions. - Tarski's axiomatization of the realsTarski's axiomatization of the realsIn 1936, Alfred Tarski set out an axiomatization of the real numbers and their arithmetic, consisting of only the 8 axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary total order over R, denoted by infix...
- Tarski's axioms for plane geometryTarski's axiomsTarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called "elementary," that is formulable in first-order logic with identity, and requiring no set theory . Other modern axiomizations of Euclidean geometry are those by Hilbert and George...
- Tarski's circle-squaring problemTarski's circle-squaring problemTarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Miklós Laczkovich in 1990; the decomposition makes heavy...
- Tarski's exponential function problemTarski's exponential function problemIn model theory, Tarski's exponential function problem asks whether the usual theory of the real numbers together with the exponential function is decidable...
- Tarski–Grothendieck set theory
- Tarski's high school algebra problemTarski's high school algebra problemIn mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught...
- Tarski–Kuratowski algorithmTarski–Kuratowski algorithmIn computability theory and mathematical logic the Tarski–Kuratowski algorithm is a non-deterministic algorithm which provides an upper bound for the complexity of formulas in the arithmetical hierarchy and analytical hierarchy....
- Tarski monster groupTarski monster groupIn mathematics, a Tarski monster group, named for Alfred Tarski, is an infinite group G, such that every proper subgroup H of G, other than the identity subgroup, is a cyclic group of order a fixed prime number p. A Tarski monster group is necessarily simple. It was shown by A. Yu...
- Tarski's plank problemTarski's plank problemIn mathematics, Tarski's plank problem is a question about coverings of convex regions in n-dimensional Euclidean space by "planks": regions between two hyperplanes. Tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region...
- Tarski's problems for free groups
- Tarski–Vaught test