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From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics
ISBN: 9780198566519 / Angielski / Twarda / 370 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope.
This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developmen...
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cena:
940,15 zł |
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The Structure of Models of Peano Arithmetic
ISBN: 9780198568278 / Angielski / Twarda / 328 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Aimed at research logicians and mathematicians, this much-awaited monograph covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before.
Aimed at research logicians and mathematicians, this much-awaited monograph covers over forty years of work on relative classification theory for non-...
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cena:
686,51 zł |
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Ockham Algebras
ISBN: 9780198599388 / Angielski / Twarda / 256 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Ockham algebras--the natural generalization of a well known and important notion of a boolean algebra--has an infinite amount of subvarieties, including those of de Morgan, Stone, and Kleene algebras. This book, the first unified account of the subject, details the many important breakthroughs that have occurred in this area of lattice theory since Berman's pioneering work in 1977. Particular emphasis is placed on Priestley's topological duality, which involves ordered sets and order-reversing maps. With its many illustrative examples and substantial bibliography, Ockham Algebras is the...
Ockham algebras--the natural generalization of a well known and important notion of a boolean algebra--has an infinite amount of subvarieties, includi...
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cena:
206,86 zł |
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Mathematical Logic
ISBN: 9780199215621 / Angielski / Miękka / 296 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is...
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logi...
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cena:
361,39 zł |
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Cellular Automata And Complexity: Collected Papers
ISBN: 9780201626643 / Angielski / Miękka / 608 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram made the radical proposal that one should instead build models that are based directly on simple computer programs. Wolfram made a detailed study of a class of such models known as cellular automata, and discovered a remarkable fact: that even when the underlying rules are very simple, the behavior they produce can be highly complex, and can mimic many features of what we see in nature. And based on this result, Wolfram began a program of research...
Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram ma...
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cena:
350,44 zł |
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Theory of Recursive Functions and Effective Computability
ISBN: 9780262680523 / Angielski / Miękka / 506 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. (Reprint of the 1967 edition) (Reprint of the 1967 edition) |
cena:
275,31 zł |
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Definability and Computability
ISBN: 9780306110399 / Angielski / Twarda / 264 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Godel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.
In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets....
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cena:
887,69 zł |
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Finitely Axiomatizable Theories
ISBN: 9780306110627 / Angielski / Twarda / 294 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This is the only monograph devoted to the expressibility of finitely axiomatizable theories, a classical subject in mathematical logic. The volume summarizes investigations in the field that have led to much of thecurrent progress, treating systematically all positive results concerning expressibility. Also included in this unique text are solutions to both the Vaught-Morely problem and the Hanf problem, and a number of new naturalquestions that provide prospects for further development of the theory.
This is the only monograph devoted to the expressibility of finitely axiomatizable theories, a classical subject in mathematical logic. The volume sum...
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cena:
806,99 zł |
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Constructive Models
ISBN: 9780306110665 / Angielski / Twarda / 293 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models.
This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some... The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within ...
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cena:
806,99 zł |
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Model-Based Reasoning in Scientific Discovery
ISBN: 9780306462924 / Angielski / Twarda / 343 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The volume is based on the papers that were presented at the Interna tional Conference Model-Based Reasoning in Scientific Discovery (MBR'98), held at the Collegio Ghislieri, University of Pavia, Pavia, Italy, in December 1998. The papers explore how scientific thinking uses models and explanatory reasoning to produce creative changes in theories and concepts. The study of diagnostic, visual, spatial, analogical, and temporal rea soning has demonstrated that there are many ways of performing intelligent and creative reasoning that cannot be described with the help only of tradi tional notions...
The volume is based on the papers that were presented at the Interna tional Conference Model-Based Reasoning in Scientific Discovery (MBR'98), held at...
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cena:
1210,50 zł |
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A Short Introduction to Intuitionistic Logic
ISBN: 9780306463945 / Angielski / Twarda / 131 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems....
Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the mat...
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cena:
564,88 zł |
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Computability and Models: Perspectives East and West
ISBN: 9780306474002 / Angielski / Twarda / 375 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in...
Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. T...
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cena:
403,47 zł |
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Numbers and Proofs
ISBN: 9780340676530 / Angielski / Miękka / 288 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. 'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then...
'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as we...
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cena:
228,74 zł |
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Adapting Proofs-As-Programs: The Curry--Howard Protocol
ISBN: 9780387237596 / Angielski / Twarda / 420 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs in constructive logic. It has been over thirty years since the paradigm was ?rst conceived. At that time, there was a belief that proofs-as-programs had the - tential for practical application to semi-automated software development. I- tial applications were mostly concerned with ?ne-grain, mathematical program synthesis. For various reasons, research interest in the area eventually tended toward more theoretic issues of constructive logic and...
This book ?nds new things to do with an old idea. The proofs-as-programs paradigm constitutes a set of approaches to developing programs from proofs i...
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cena:
605,23 zł |
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Mathematical Problems from Applied Logic I: Logics for the Xxist Century
ISBN: 9780387286884 / Angielski / Twarda / 348 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. An overview of the current state as well as open problems and perspectives are clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics, and computability theory. The book contains interesting contributions concerning the role... Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from... |
cena:
605,23 zł |
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Notes on Set Theory
ISBN: 9780387287225 / Angielski / Twarda / 278 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and... The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is ... |
cena:
322,77 zł |
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Notes on Set Theory
ISBN: 9780387287232 / Angielski / Miękka / 278 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and... The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is ... |
cena:
262,25 zł |
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Problems and Theorems in Classical Set Theory
ISBN: 9780387302935 / Angielski / Twarda / 516 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. Although the ?rst decades of the 20th century saw some strong debates on set theory and the foundation of mathematics, afterwards set theory has turned into a solid branch of mathematics, indeed, so solid, that it serves as the foundation of the whole building of mathematics. Later generations, honest to Hilbert s dictum, No one can chase us out of the paradise that Cantor has created for us proved countless deep and interesting theorems and also applied the methods of set theory to various problems in algebra, topology, in?nitary combinatorics, and real analysis. The invention of forcing...
Although the ?rst decades of the 20th century saw some strong debates on set theory and the foundation of mathematics, afterwards set theory has turne...
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cena:
282,42 zł |
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Techniques of Constructive Analysis
ISBN: 9780387336466 / Angielski / Miękka / 215 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the... This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text cov... |
cena:
262,25 zł |
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Mathematical Problems from Applied Logic II: Logics for the Xxist Century
ISBN: 9780387692449 / Angielski / Twarda / 354 str. Termin realizacji zamówienia: ok. 5-8 dni roboczych. "Mathematical Problems from Applied Logic II" presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. Fields covered include: logic of provability, applications of computability theory to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based... "Mathematical Problems from Applied Logic II" presents chapters from selected, world renowned, logicians. Important topics of logic are discussed f... |
cena:
403,47 zł |
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