Books in Mathematical logic and foundations

The Nuts and Bolts of Proofs

4th Edition
November 25, 2011
Antonella Cupillari
English
Paperback
9 7 8 0 1 2 3 8 2 2 1 7 8
eBook
9 7 8 0 1 2 3 8 2 2 1 8 5

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable.

Logic, Methodology and Philosophy of Science VI

1st Edition
October 10, 2011
J.J. Cohen + 3 more
English
eBook
9 7 8 0 0 8 0 9 6 0 3 0 2

Logic, Methodology and Philosophy of Science VI presents the results of recent research into the foundations of science. The volume contains invited papers presented at the Congress, covering the areas of Logic, Mathematics, Physical Sciences, Biological Sciences and the Humanities.

Logic Colloquium '84

1st Edition
October 10, 2011
J.B. Paris + 2 more
English
eBook
9 7 8 0 0 8 0 9 6 0 4 3 2

This proceedings volume contains most of the invited talks presented at the colloquium. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications of mathematical logic to complexity theory. The volume contains both surveys by acknowledged experts and original research papers presenting advances in these disciplines.

Axiomatic Set Theory

1st Edition
Volume 51
August 30, 2011
R.B. Chuaqui
English
eBook
9 7 8 0 0 8 0 8 7 1 6 2 2

Fundamentals of Generalized Recursion Theory

1st Edition
August 18, 2011
M. Fitting
English
eBook
9 7 8 0 0 8 0 9 6 0 3 1 9

Theory of Relations

1st Edition
August 18, 2011
R. Fraïssé
English
eBook
9 7 8 0 0 8 0 9 6 0 4 1 8

The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey's theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver's embeddability theorem for scattered chains, using Nash-Williams' better quasi-orderings, barriers and forerunning.The second part (chapters 9 to 12) extends to general relations the main notions and results from order-type theory. An important connection appears with permutation theory (Cameron, Pouzet, Livingstone and Wagner) and with logics (existence criterion of Pouzet-Vaught for saturated relations). The notion of bound of a relation (due to the author) leads to important calculus of thresholds by Frasnay, Hodges, Lachlan and Shelah. The redaction systematically goes back to set-theoretic axioms and precise definitions (such as Tarski's definition for finite sets), so that for each statement it is mentioned either that ZF axioms suffice, or what other axioms are needed (choice, continuum, dependent choice, ultrafilter axiom, etc.).

Foundations of Infinitesimal Stochastic Analysis

1st Edition
August 18, 2011
K.D. Stroyan + 1 more
English
eBook
9 7 8 0 0 8 0 9 6 0 4 2 5

This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.