Birkhoffs completeness theorem
Birkhoff's completeness theorem Equational logic is a formal system for reasoning with equations. It has simple rules for manipulating equations, based on the reflexivity, symmetry, transivity of equality and the substitution of equal terms into equations. Birkhoff's completeness theorem says that an equation e is provable in equational logic from the equations in a set E if and only if e is true in all algebras that satisfy the equations in the set E. Related to the theorem is the fact that a class of algebras is definable as the class of all models of some set of equations if and only if the class is closed under constructing subalgebras, homomorphic images, and direct products. These results were proved by G. Birkhoff in 1935. See also equational specification, term rewriting system.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Birkhoffs completeness theorem." A Dictionary of Computing. . Encyclopedia.com. 18 Oct. 2018 <http://www.encyclopedia.com>.
"Birkhoffs completeness theorem." A Dictionary of Computing. . Encyclopedia.com. (October 18, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/birkhoffscompletenesstheorem
"Birkhoffs completeness theorem." A Dictionary of Computing. . Retrieved October 18, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/birkhoffscompletenesstheorem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.