Welcome to the web site:  predicate-logic.org

Classical first-order Predicate Logic represents a firm foundation for mathematics. Actually, the logic represents pivot for human intelligence as well as for artificial intelligence. Most important mathematical theories can be formally exact founded on the base of first-order Predicate Calculus with equality (while, some logicians point out logical incompleteness of such approach). 

Approximately twenty year ago, an Universal construction of finitely axiomatizable theories was described showing that, in terms of the majority of natural model-theoretic properties, expressive power of finitely axiomatizable theories in first-order Predicate Logic is exactly the same as that of recursively axiomatizable theories. A lot of natural questions concerning finitely axiomatizable theories were solved by way of their reduction to essentially more easy case of recursively axiomatizable theories.

Main goal of this website is to present a new monograph by Mikhail Peretyat'kin, "Expressive Power of First-Order Predicate Logic", which is currently in final stage of preparation. Its title page is supposed to be approximately the following:

The monograph includes detailed and closed description of available constructions of finitely axiomatizable theories and represents characterization of general structure of Tarski-Lindenbaum algebra of first-order Predicate Calculus of an arbitrary finite rich signature. Results concerning global structure of Predicate Logic are completely new; moreover, they represent main top result of the whole book, subordinating its text to this particular result. The direction of the book is strictly subordinated to the purpose to have as complete and closed text as possible, which would contain the results regarded to expressive possibilities of first-order Predicate Logic. On the other hand, the text of the book is rigidly limited to this only purpose, including minimum of necessary.

Demonstration of presentation material concerning both main results and structure of the book can be seen in the following PDF-file:

Presentation5may2010.pdf

 As for previous monograph in this direction, it is shown below (Mikhail Peretyatkin, "Finitely axiomatizable theories", 297 pages, 1997; an equivalent book in Russian is also available, 1997). It has played role of some starting prototype for given new book. 

           

Text of the new book is essentially more complete, detailed, and structured, providing detailed proofs for all results included in this new book.

This page was last updated on 05/19/10.