#jsDisabledContent { display:none; } My Account | Register | Help

# Principles of Mathematical Logic

Article Id: WHEBN0002134047
Reproduction Date:

 Title: Principles of Mathematical Logic Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Principles of Mathematical Logic

Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge der theoretischen Logik,[1] on elementary mathematical logic. The 1928 first edition thereof is considered the first elementary text clearly grounded in the formalism now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory.

The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The first problem was answered in the negative by Alonzo Church in 1936. The second was answered affirmatively by Kurt Gödel in 1929.

The text also touched on set theory and relational algebra as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of Principia Mathematica, long popular in the English speaking world.

## References

• David Hilbert and Wilhelm Ackermann (1928). Grundzüge der theoretischen Logik (Principles of Mathematical Logic). Springer-Verlag, ISBN 0-8218-2024-9. This text went into four subsequent German editions, the last in 1972.
• Hendricks, Neuhaus, Petersen, Scheffler and Wansing (eds.) (2004). First-order logic revisited. Logos Verlag, ISBN 3-8325-0475-3. Proceedings of a workshop, FOL-75, commemorating the 75th anniversary of the publication of Hilbert and Ackermann (1928).

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.