10 Facts About Mathematical logic

However, it can include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.

Since its inception, mathematical logic has both contributed to and has been motivated by the study of foundations of mathematics.

Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics.

Theories of Mathematical logic were developed in many cultures in history, including China, India, Greece and the Islamic world.

Greek methods, particularly Aristotelian Mathematical logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia.

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Intuitionistic Mathematical logic was developed by Heyting to study Brouwer's program of intuitionism, in which Brouwer himself avoided formalization.

Kleene's work with the proof theory of intuitionistic Mathematical logic showed that constructive information can be recovered from intuitionistic proofs.

Mathematical logic noted that his methods were equally applicable to algebraically closed fields of arbitrary characteristic.

Computer scientists often focus on concrete programming languages and feasible computability, while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.

Formal calculi such as the lambda calculus and combinatory Mathematical logic are now studied as idealized programming languages.