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Herbert Bruce Enderton (April 15, 1936 – October 20, 2010) [1] was an American mathematician. He was a Professor Emeritus of Mathematics at UCLA and a former member of the faculties of Mathematics and of Logic and the Methodology of Science at the University of California, Berkeley .
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.
Enderton, Herbert B. (1972), A mathematical introduction to logic, Academic Press, New York-London, p. 147, MR 0337470. Łoś, Jerzy (1954), "On the categoricity in power of elementary deductive systems and some related problems", Colloquium Mathematicum, 3: 58–62, MR 0061561.
Herbert B. Enderton, 2001, A Mathematical Introduction to Logic Second Edition, Harcourt Academic Press, Burlington MA, ISBN 978-0-12-238452-3. Audun Jøsang, 2016, Subjective Logic; A formalism for Reasoning Under Uncertainty Springer, Cham, ISBN 978-3-319-42337-1
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is ...
Enderton, Herbert (2001), A mathematical introduction to logic (2nd ed.), Academic Press, ISBN 978-0-12-238452-3 Keisler, H. J. (1982), "Fundamentals of model theory", in Barwise, Jon (ed.), Handbook of Mathematical Logic , Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland, ISBN 978-0-444-86388-1
PM, according to its introduction, had three aims: (1) to analyze to the greatest possible extent the ideas and methods of mathematical logic and to minimize the number of primitive notions, axioms, and inference rules; (2) to precisely express mathematical propositions in symbolic logic using the most convenient notation that precise ...
A parenthetical remark from Enderton: A Mathematical Introduction to Logic (2001 edition), p. 80: "Structures are sometimes called interpretations, but we prefer to reserve that word for another concept, to be encountered in Section 2.7." Section 2.7 is called "Interpretations Between Theories" and refers to interpretation (model theory).
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