증명 이론

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위키데이터

• ID : Q852732

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1. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity.
2. In parallel to the rise and fall of Hilbert's program, the foundations of structural proof theory were being founded.
3. Structural proof theory is the subdiscipline of proof theory that studies the specifics of proof calculi.
4. The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II.
5. Proof theory has turned into a fascinating area of research at the intersection of philosophy, mathematics and, increasingly, computer science.
6. Sieg's papers in proof theory fall into three groups.
7. Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself.
8. Proof theory can be described as the study of the general structure of mathematical proofs, and of arguments with demonstrative force as encountered in logic.
9. Von Neumann was the key character in the reception of Gödel's results: He interrupted his lectures on Hilbert's proof theory in Berlin in the fall of 1930 to explain the new discoveries.
10. The first observation is that actual proofs are not based on axioms expressed in a logical language, as in Hilbert's axiomatic proof theory.
11. The work marked the beginning of ordinal proof theory.
12. Bernays concludes the outline by suggesting, “This would be followed by the development of proof theory”.
13. The third part of these lectures is entitled The grounding of the consistency of arithmetic by Hilbert’s new proof theory.
14. As this is a tool of utmost importance in proof theory, an outline of the underlying ideas will be discussed next.
15. The two aspects together opened a new era for proof theory and mathematical logic with the goal of proving the consistency of analysis.
16. Proof theory comprises standard methods of formalization of the content of mathematical theories.
17. Proof theory makes extensive use of algebraic methods in the form of model theory.
18. In terms of constructions of model theory it is possible to give simple criteria for many concepts of interest to proof theory.
19. What are, or should be the aims of proof theory?
20. I would agree with him that people no longer look to proof theory for epistemological security (like Hilbert).
21. Are there any neglected directions in proof theory?
22. In what ways can or should proof theory relate to other parts of logic/foundations/mathematics/computer science/linguistics/etc.?
23. This chapter presents an exposition of certain themes in proof theory.
24. In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs.
25. Gentzen was able to prove in terms of sequent calculi some of the most basic results of proof theory.
26. Gentzen and other logicians also used proof theory to study Hilbert’s original question of the possibility of proofs of the consistency of logical and mathematical systems.
27. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations.
28. Present the duality between model theory and proof theory in a philosophically illuminating and clear fashion.
29. How Proof Theory, Rules and Meaning hangs together.
30. Tools: in which core concepts from proof theory are introduced.
31. This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects.
32. In the last two decades proof theory has become increasingly important for computer science, and proof theory and theoretical computer science are nowadays considered as being very closely related.
33. The Proof Theory Virtual Seminar presents talks by leading researchers from all areas of proof theory.
34. The workshop aims at bringing together researchers in proof theory and rewriting to facilitate the exchange of ideas between these tightly connected fields.
35. I will relate the results of my investigations into the proof theory of the unfolding of ID1, the schematic system of one arithmetical inductive definition.
36. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.
37. Five years ago I had the pleasure of reviewing Menzler-Trott’s biographical study of Gerhard Gentzen, the main player on the scene in the early days of proof theory.
38. The development of proof theory enabled the mathematical community to introduce their own work, (informal) mathematical proofs, to thorough meta-mathematical treatment.

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위키데이터

• ID : Q852732