ganiteeya tarkashaastr

ganiteeya tarkashaastr (Mathematical logic) ganit ki shaakha hai kiska sanganak vigyaan evam daarshanik tarkashaastr se nikat ka sambandh hai. tarkashaastr ka ganiteeya adhyayan tatha ganit ke anya vidhaaon mein tarkashaastr (formal logic) ke anuprayog dono hi iske antargat aate hain.

praaya: ganiteeya tarkashaastr ko samuchchaya siddhaant, model siddhaant (model theory), rikrsan siddhaant (recursion theory) tatha siddhi siddhaant (proof theory) naamak kshetron mein vibhkt kiya jaata hai.

itihaas

ganiteeya tarkashaastr apne aarambhakaal se hi ganit ke aadhaarashilaaon (foundations of mathematics) ke adhyayan mein sahaayak siddh hua hai tatha usase prerana paata raha hai. iska adhyayan 19veen shataabdi ke antim dinon mein aarambh hua. sabse pehle iske liye jyaamiti, ankaganit aur vishleshan ke svayansiddhon (axioms) ka vikaas hua. 20veen shati ke aarambhik dinon mein David hilbart ne ise gati pradaan ki. unhone 'faaundeshanal siddhaanton ki samagrata' (consistency of foundational theories) ko siddh karne ka program chalaaya. kurt godel (Kurt Göadel), garahard jentajen (Gerhard Gentzen) evam anya logon ne is kaarya ko aur aage badhaaya. samuchchaya siddhaant ke kshetr mein aur kaarya hue jisse yeh pradarshit hua ki lagbhag sampoorn saamaanya ganit ko samuchchayon ke roop mein 'faurmalaaij' kiya ja sakta hai.

baahari kadiyaaain

Mathematical Logic around the world
Polyvalued logic
forall x: an introduction to formal logic, by P.D. Magnus, is a free textbook.
A Problem Course in Mathematical Logic, by Stefan Bilaniuk, is another free textbook.
Detlovs, Vilnis, and Podnieks, Karlis (University of Latvia) Introduction to Mathematical Logic. A hyper-textbook.
Stanford Encyclopedia of Philosophy: Classical Logic – by Stewart Shapiro.
Stanford Encyclopedia of Philosophy: First-order Model Theory – by Wilfrid Hodges.
The London Philosophy Study Guide offers many suggestions on what to read, depending on the student's familiarity with the subject: