Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Recursive Functions --- Incompleteness

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Gödel's theorem --- Incompleteness theorems --- Social prediction

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Incompleteness theorems --- Recursion theory --- Theorems, Incompleteness --- Logic, Symbolic and mathematical --- Constructive mathematics --- Proof theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

Incompleteness theorem --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Incompleteness theorems. --- Theorems, Incompleteness --- Constructive mathematics --- Proof theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"Among the many expositions of Godel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Godel

Mathematical logic --- Philosophy of science --- Gödel's theorem --- Gödel's theorem. --- Incompleteness theorems. --- Gödel's theorem --- Incompleteness theorems --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Logic, Symbolic and mathematical --- Number theory --- Decidability (Mathematical logic) --- Theorems, Incompleteness --- Constructive mathematics --- Proof theory --- Foundations --- Logique mathématique --- Gödel, Kurt F., 1906 --- -Logique mathématique --- Logique mathematique --- Theorie de la preuve --- -Gödel's theorem.