metalogic

Table of Contents

Introduction
Nature, origins, and influences of metalogic
- Syntax and semantics
- The axiomatic method
- Logic and metalogic
- Semiotic
- Influences in other directions
Nature of a formal system and of its formal language
- Example of a formal system
  - Formation rules
  - Axioms and rules of inference
- Truth definition of the given language
Discoveries about formal mathematical systems
- The two incompleteness theorems
- Decidability and undecidability
- Consistency proofs
Discoveries about logical calculi
- The propositional calculus
- The first-order predicate calculus
- The Löwenheim-Skolem theorem
- The completeness theorem
- The undecidability theorem and reduction classes
Model theory
- Background and typical problems
  - Satisfaction of a theory by a structure: finite and infinite models
  - Elementary logic
  - Nonelementary logic and future developments
- Characterizations of the first-order logic
- Generalizations and extensions of the Löwenheim-Skolem theorem
- Ultrafilters, ultraproducts, and ultrapowers

References & Edit History Related Topics

Images

For Students

metalogic summary

Read Next

Frowning little girl. Angry annoyed

Is Body Language Universal?

Happy, smiling, flying pig

7 Everyday English Idioms and Where They Come From

Skyline Barcelona at sunset, Spain

Is Castilian Spanish Spoken with a Lisp?

Student girl writing formulas on transparent wall

The Bizarre Origins of the Words Nerd and Geek

Discover

King Cobra snake in Malaysia. (reptile)

9 of the World’s Deadliest Snakes

Four year old boy with grandfather and father lighting Hanukkah menorah. Photo taken on: December 21st, 2009

Which Is Correct: Hanukkah or Chanukah?

The Prado Museum facade at the Diego Velaszquez memorial. Established in 1819, the museum is considered the best collection of Spanish art and one of the world's finest collections of European art. Madrid, Spain

20 Paintings You Have to Visit at the Museo del Prado in Madrid

Town of Sisimiut located on the coast of the Davis Strait on Kangerluarsunnguaq Bay, Greenland

The Largest Islands in the World

Srinivasa Ramanujan, Indian mathematician and autodidact.

6 Interesting Facts about Srinivasa Ramanujan

Ice Sledge Hockey, Hockey Canada Cup, USA (left) vs Canada, 2009. UBC Thunderbird Arena, Vancouver, BC, competition site for Olympic ice hockey and Paralympic ice sledge hockey. Vancouver 2010 Olympic and Paralympic Winter Games, Vancouver Olympics

10 Best Hockey Players of All Time

Nativity Scene, Adoration of the Magi, Church of the Birth of the Virgin Mary, Montenegro

Why Is Christmas in December?

metalogic: Media

Images

David Hilbert

David Hilbert

David Hilbert.

Rudolf Carnap

Rudolf Carnap

Rudolf Carnap, 1960.

Courtesy of the University of California, Los Angeles

Alan Turing

Alan Turing

Alan Turing, 1951.

Science History Images/Alamy

VIEW MORE in these related Britannica articles: