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The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions: Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented. Exact combinatorial optimization algorithms, in which the complexity relative to the source data is characterized by a low, or even first degree, polynomial (1 article). III. Applications of mathematical logic and the theory of algorithms (2 articles). The first article deals with the Jacobian and M. Kontsevich’s conjectures, and algorithmic undecidability; for these purposes, non-standard analysis is used. The second article provides a quantitative description of the balance and adaptive resource of a human. Submissions are invited for the next issue "Mathematical Logic and Its Applications 2021"
Research & information: general --- Mathematics & science --- definability --- nonconstructible reals --- projective hierarchy --- generic models --- almost disjoint forcing --- Harvey Friedman’s problem --- almost-disjoint forcing --- universal algebraic geometry --- affine algebraic geometry --- elementary equivalence --- isotypic algebras --- first order rigidity --- Ind-group --- affine spaces --- automorphisms --- free associative algebras --- Weyl algebra automorphisms --- polynomial symplectomorphisms --- deformation quantization --- infinite prime number --- semi-inner automorphism --- embeddability of varieties --- undecidability --- noncommutative Gröbner-Shirshov basis --- finitely presented algebraic systems --- algorithmic unsolvability --- turing machine --- discrete optimization --- exact algorithm --- additively exact algorithm --- graph transformation --- graph of degree 2 --- chain-cycle graph --- operation cost --- minimization of total cost --- definability of definable --- tarski problem --- type theoretic hierarchy --- adaptive resource --- resilience --- resistance --- tipping point --- theory of catastrophes
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The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions: Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented. Exact combinatorial optimization algorithms, in which the complexity relative to the source data is characterized by a low, or even first degree, polynomial (1 article). III. Applications of mathematical logic and the theory of algorithms (2 articles). The first article deals with the Jacobian and M. Kontsevich’s conjectures, and algorithmic undecidability; for these purposes, non-standard analysis is used. The second article provides a quantitative description of the balance and adaptive resource of a human. Submissions are invited for the next issue "Mathematical Logic and Its Applications 2021"
definability --- nonconstructible reals --- projective hierarchy --- generic models --- almost disjoint forcing --- Harvey Friedman’s problem --- almost-disjoint forcing --- universal algebraic geometry --- affine algebraic geometry --- elementary equivalence --- isotypic algebras --- first order rigidity --- Ind-group --- affine spaces --- automorphisms --- free associative algebras --- Weyl algebra automorphisms --- polynomial symplectomorphisms --- deformation quantization --- infinite prime number --- semi-inner automorphism --- embeddability of varieties --- undecidability --- noncommutative Gröbner-Shirshov basis --- finitely presented algebraic systems --- algorithmic unsolvability --- turing machine --- discrete optimization --- exact algorithm --- additively exact algorithm --- graph transformation --- graph of degree 2 --- chain-cycle graph --- operation cost --- minimization of total cost --- definability of definable --- tarski problem --- type theoretic hierarchy --- adaptive resource --- resilience --- resistance --- tipping point --- theory of catastrophes
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The issue "Mathematical Logic and Its Applications 2020" contains articles related to the following three directions: Descriptive Set Theory (3 articles). Solutions for long-standing problems, including those of A. Tarski and H. Friedman, are presented. Exact combinatorial optimization algorithms, in which the complexity relative to the source data is characterized by a low, or even first degree, polynomial (1 article). III. Applications of mathematical logic and the theory of algorithms (2 articles). The first article deals with the Jacobian and M. Kontsevich’s conjectures, and algorithmic undecidability; for these purposes, non-standard analysis is used. The second article provides a quantitative description of the balance and adaptive resource of a human. Submissions are invited for the next issue "Mathematical Logic and Its Applications 2021"
Research & information: general --- Mathematics & science --- definability --- nonconstructible reals --- projective hierarchy --- generic models --- almost disjoint forcing --- Harvey Friedman’s problem --- almost-disjoint forcing --- universal algebraic geometry --- affine algebraic geometry --- elementary equivalence --- isotypic algebras --- first order rigidity --- Ind-group --- affine spaces --- automorphisms --- free associative algebras --- Weyl algebra automorphisms --- polynomial symplectomorphisms --- deformation quantization --- infinite prime number --- semi-inner automorphism --- embeddability of varieties --- undecidability --- noncommutative Gröbner-Shirshov basis --- finitely presented algebraic systems --- algorithmic unsolvability --- turing machine --- discrete optimization --- exact algorithm --- additively exact algorithm --- graph transformation --- graph of degree 2 --- chain-cycle graph --- operation cost --- minimization of total cost --- definability of definable --- tarski problem --- type theoretic hierarchy --- adaptive resource --- resilience --- resistance --- tipping point --- theory of catastrophes --- definability --- nonconstructible reals --- projective hierarchy --- generic models --- almost disjoint forcing --- Harvey Friedman’s problem --- almost-disjoint forcing --- universal algebraic geometry --- affine algebraic geometry --- elementary equivalence --- isotypic algebras --- first order rigidity --- Ind-group --- affine spaces --- automorphisms --- free associative algebras --- Weyl algebra automorphisms --- polynomial symplectomorphisms --- deformation quantization --- infinite prime number --- semi-inner automorphism --- embeddability of varieties --- undecidability --- noncommutative Gröbner-Shirshov basis --- finitely presented algebraic systems --- algorithmic unsolvability --- turing machine --- discrete optimization --- exact algorithm --- additively exact algorithm --- graph transformation --- graph of degree 2 --- chain-cycle graph --- operation cost --- minimization of total cost --- definability of definable --- tarski problem --- type theoretic hierarchy --- adaptive resource --- resilience --- resistance --- tipping point --- theory of catastrophes
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Band III der Hausdorff-Edition enthält Hausdorffs Band „Mengenlehre", seine veröffentlichten Arbeiten zur deskriptiven Mengenlehre und Topologie sowie zahlreiche einschlägige Studien aus dem Nachlaß. Sein Buch „Mengenlehre" erlangte besonders dadurch historische Bedeutung, als darin erstmals eine monographische Darstellung des damals aktuellen Standes der deskriptiven Mengenlehre gegeben wurde. Es ist hier von Spezialisten dieses Gebietes sorgfältig kommentiert worden. Auch die veröffentlichten Arbeiten sind mit ausführlichen Kommentaren versehen. Besonders umfassend ist in diesem Band der Edition der Nachlaß Hausdorffs berücksichtigt. Hingewiesen sei insbesondere auf seinen zahlreichen originellen Studien zu Themen der deskriptiven Mengenlehre und auf seine damals sehr originelle Vorlesung über algebraische Topologie vom Sommersemester 1933.
Mathematics. --- History. --- Mathematical logic. --- Topology. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Topology. --- Mathematics, general.
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