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Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert
David Hilbert

David Hilbert was a Germany mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries....
's and Wilhelm Ackermann
Wilhelm Ackermann

Wilhelm Friedrich Ackermann was a Germany mathematician best known for the Ackermann function, an important example in the theory of computation....
's classic text Grundzüge der theoretischen Logik, 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
First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
 (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status.






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Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert
David Hilbert

David Hilbert was a Germany mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries....
's and Wilhelm Ackermann
Wilhelm Ackermann

Wilhelm Friedrich Ackermann was a Germany mathematician best known for the Ackermann function, an important example in the theory of computation....
's classic text Grundzüge der theoretischen Logik, 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
First-order logic

First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
 (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now the core formalism of all 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
Entscheidungsproblem

In mathematics, the Entscheidungsproblem is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for an algorithm that will take as input a description of a formal language and a mathematical statement in the language and produce as output either "True" or "False" according to whether the statement is true or false....
 (decision problem
Decision problem

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters....
) for FOL, and also asked whether that logic was complete
Gödel's completeness theorem

G?del's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic Provability logic in first-order logic....
 (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
Alonzo Church

Alonzo Church was an United States mathematician and list of logicians who made major contributions to mathematical logic and the foundations of theoretical computer science....
 in 1936. The second was answered affirmatively by Kurt Gödel
Kurt Gödel

Kurt G?del was an Austrian-United States logician, mathematician and philosopher. One of the most significant logicians of all time, G?del made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A....
 in 1929.

The text also touched on set theory
Set theory

Set theory is the branch of mathematics that studies Set , which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics....
 and relational algebra
Relational algebra

Relational algebra, an offshoot of first-order logic , deals with a set of mathematical relations Closure under operators. Operators operate on one or more relations to yield a relation....
 as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of Principia Mathematica
Principia Mathematica

The Principia Mathematica is a 3-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910?1913....
, long popular in the English speaking world.