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Barwise, along with his former colleague at Stanford John Etchemendy, was the author of the popular logic textbook Language, Proof and Logic. Unlike the Handbook of Mathematical Logic, which was a survey of the state of the art of mathematical logic circa 1975, and of which he was the editor, this work targeted elementary logic. The text is ...
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory , proof theory , set theory , and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics.The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron.
The book begins with a historical overview of the long struggles with the parallel postulate in Euclidean geometry, [3] and of the foundational crisis of the late 19th and early 20th centuries, [6] Then, after reviewing background material in real analysis and computability theory, [1] the book concentrates on the reverse mathematics of theorems in real analysis, [3] including the Bolzano ...
The notion of analytic proof was introduced into proof theory by Gerhard Gentzen for the sequent calculus; the analytic proofs are those that are cut-free.His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is slightly more complex—the analytic proofs are the normal forms, which are related to the notion of normal form in term ...
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. [5] The field was founded by Harvey Friedman . Its defining method can be described as "going backwards from the theorems to the axioms ", in contrast to the ordinary mathematical practice of deriving ...
Computational logic is the branch of logic and computer science that studies how to implement mathematical reasoning and logical formalisms using computers. This includes, for example, automatic theorem provers , which employ rules of inference to construct a proof step by step from a set of premises to the intended conclusion without human ...
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms ", in contrast to the ordinary mathematical practice of deriving theorems from axioms.
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