Tarski's Axioms

Tarski'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 (Tarski 1959). Other modern axiomizations of Euclidean geometry are those by Hilbert and George Birkhoff.

Read more about Tarski's Axioms:  Overview, The Axioms, Discussion, Comparison With Hilbert

Other articles related to "tarski":

List Of Things Named After Alfred Tarski - Other Mathematics-related Things
... Banach–Tarski paradox Lindenbaum–Tarski algebra Jónsson–Tarski duality Gödel–McKinsey–Tarski translation The semantic theory of truth is ... Tarski's axiomatization of the reals Tarski's axioms for plane geometry Tarski's circle-squaring problem Tarski's exponential function problem Tarski–Gro ...
List Of Things Named After Alfred Tarski - Theorems
... Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski's undefinability theorem Tarski–Seidenberg theorem Some fixed point theorems, usually variants of the Kleene fixed-p ... Tarski's theorem ...
Tarski's Plank Problem
... In mathematics, Tarski's plank problem is a question about coverings of convex regions in n-dimensional Euclidean space by "planks" regions between two ... Tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region ...
Philosophy Of Logic - Truth - Tarski's Definition of Truth
... See- Semantic theory of truth#Tarski's Theory T-schema Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions Self-reference2.1 Consequences of the ...
Decidability (logic) - Some Decidable Theories
... first-order theory of Boolean algebras, established by Alfred Tarski in 1949 ... theory of algebraically closed fields of a given characteristic, established by Tarski in 1949 ... The first-order theory of real-closed ordered fields, established by Tarski in 1949 ...

Famous quotes containing the word axioms:

    The axioms of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.
    Ralph Waldo Emerson (1803–1882)