Godel's Incompleteness Theorems

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems.

Approximation Theorems of Mathematical Statistics
This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory.

This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results.

During the recent years the interest in limit theorems for dependent random variables has considerably grown being stimulated both by requirements of probability theory and by many applied disciplines. A special place among such disciplines belongs to statistical physics whose mathematical apparatus for a long time has been developing regardless the probability theory. However recently a process of mutual understanding between the specialists of this two fields started to develop. This resulted in a burst of activity for the benefit of both the subjects. For instance, the concept of Gibbs random field which has originated in statistical physics became a powerful stimulus for development of the theory of random fields while the Gibbsian fields themselves turned out to be excellent object for application of many general probabilistic results.