ATR meaning in Maths ?

Answer:

What is Arithmetical Transfinite Recursion mean?

In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics.

A precursor to second-order arithmetic that involves third-order parameters was introduced by David Hilbert and Paul Bernays in their book Grundlagen der Mathematik. The standard axiomatization of second-order arithmetic is denoted by Z2.

Second-order arithmetic includes, but is significantly stronger than, its first-order counterpart Peano arithmetic. Unlike Peano arithmetic, second-order arithmetic allows quantification over sets of natural numbers as well as numbers themselves. Because real numbers can be represented as (infinite) sets of natural numbers in well-known ways, and because second-order arithmetic allows quantification over such sets, it is possible to formalize the real numbers in second-order arithmetic. For this reason, second-order arithmetic is sometimes called “analysis” (Sieg 2013, p. 291).

Second-order arithmetic can also be seen as a weak version of set theory in which every element is either a natural number or a set of natural numbers. Although it is much weaker than Zermelo–Fraenkel set theory, second-order arithmetic can prove essentially all of the results of classical mathematics expressible in its language.

A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z2). Such subsystems are essential to reverse mathematics, a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength. Much of core mathematics can be formalized in these weak subsystems, some of which are defined below. Reverse mathematics also clarifies the extent and manner in which classical mathematics is nonconstructive.

reference

Full Form	Category
Action Tracking Register	Academic & Science
Adaptive Temporal Recursion	Academic & Science
AutoThermal Reforming	Academic & Science
Absolute Time Reference	Academic & Science
Advanced Test Reactor	Academic & Science
Atar	Airport Code
Acid Test Ratio	Banking
Auto Parts Ring	Business
Aptar Group, Inc.	Business
Automatic Tampon Remover	Business
Avion de Transport Regional	Business
Accuracy Timeliness Responsiveness	Business
Advanced Technologies and Research	Business
Aerei da Trasporto Regionale	Business
Astron Corporation, Limited	Business
Accounting to Reporting	Business
Atari Teenage Riot	Community
All That Remains	Community
Absent Teacher Reserve	Community
African Traditional Religion	Community
Answer To Reset	Computer Assembly Language
Acceptance Test Review	Computing
Adaptive Transformation	Computing
Automatic Terminal Recognition	Computing
Apollo Token Ring	Computing
Audio Tape Recorder	Computing
Alternate Trunk Routing	Computing
Alexa Traffic Rank	Computing
All Terrain Racing	Computing
Andy's Techno Rules	Computing
Antenna Test Range	Electronics
Attenuated Total Reflectance	Electronics
Alpha Test Realm	General
Advanced Term Registration	General
Abe T Rosenthal	General
Auto Transformer Rectifier	General
Accumulated Time Record	General
and the Role	General
All Terrain Road	General
Arkansas Trucking Report	General
Automobiles Transport Rapide	General
Autoliv Turkey	General
Average Treatment Rate	General
Automated Target Recognition	General
Automated Traffic Recorder	General
Active Time Report	General
AGS to RHIC	General
Aviation Training Relocation	General
Acceptance Test Report	General
Assess Transform Reach	General
Attenuated Total Reflection	General
Accommodated Test Request	General
Arena Technical Resources	General
Articulated Tail Rotor	General
Automatic Locking Retractors	General
Amicale du Tracteur Renault	General
Automatic Traffic Recorder	General
Autotrack	General
Automatic Transmission Relay	General
Automotive Tradition	General
Accord Type R	General
Access To Recovery	General
Advanced Thermo Resin	General
Appropriate Technical Resources	General
Transmission Remanufacturing	General
Air Transport Rated	General
American Technical Resources	General
All Things Rock	General
Annual Temperature Range	General
The Ags To Rhic	General
A Tape Reader	General
Ataxia Telangiectasia and Rad3	General
Ability to Repay	General
All Terrain Rig	General
Avions De Transport Regional	Governmental
All Terrain Radial tire	Governmental
Action Taken Report	Governmental
After The Revolution	Governmental
Americans for Tax Reform	Income Tax
ATTAR	Indian Railway Station
Art Therapist Registered	Jobs
Arithmetical Transfinite Recursion	Maths
Almost Totally Real	Maths
Additional Testing Required	Medical
Achilles Tendon Reflex	Medical
Atrophy	Medical
Acute Transfusion Reaction	Medical
Automatic Tampon Removal	Medical
Advanced Tongue Root	Medical
Ataxia Telangiectasia and Rad3 related	Medical
Anti Tank Rifle	Military and Defence
Attack The Rim	Military and Defence
Automatic Target Recognition	Military and Defence
Advanced Tactical Radar	Military and Defence
Annual Training Requirement	Military and Defence
Attrition Reserve	Military and Defence
Auxiliary Tug and Rescue	Military and Defence
Attack The Radical	Military and Defence
Average True Range	Military and Defence
All Terrain Rifle	Military and Defence
Air Transport Rack	Military and Defence
Alaska Trauma Registry	Military and Defence
Army Training Regiment	Military and Defence
Anglican Theological Review	News & Entertainment
Avions Transport Regional	Regional
Alliance Terminal Railroad	Regional
Above The Rest	Space Science
Advanced Technology Recycling	Sports
Australian Tournament Rankings	Sports
Automatic Ticket Resolution	Sports
Adventure Tour Race	Sports
Average Trading Range	Stock Exchange
Albemarles Technology Resource	Technology
Advanced Technology and Research	Technology
Advanced Telecommunications Research	Telecommunication
Andaman Trunk Road	Transport & Travel
Atar Airport	Transport & Travel
Atractyloside	Trees & Plants
Avions De Transport R	Uncategorized